Contents of the Current Volume
Volume 1
metric Geometry and minimal SubmanifoldS
Foreword by Shing-Tung Yau ........................................................................................... XV
Preface by the Editors ....................................................................................................... XXI
Commentary by Richard Hamilton ............................................................................... XXIII
Commentary by William H. Meeks III .......................................................................... XXV
Commentary by Richard Schoen ....................................................................................XXXI
Commentary by Leon Simon .....................................................................................XXXVII
Articles
※On the fundamental group of compact manifolds of non-positive curvature§,
Annals of Mathematics 93 (1971) 579每585. ................................................................... 1
(with H. Lawson), ※Compact manifolds of nonpositive curvature§, J. Differential
Geom. 7 (1972), 211每228.......................................................................................9
※Some global theorems on non-complete surfaces§, Comment. Math. Helv. 48
(1973), 177每187. ................................................................................................27
(with H. Lawson), ※Scalar curvature, non-abelian group actions, and the degree of
symmetry of exotic spheres§, Comment. Math. Helv. 49 (1974), 232每244...................39
※Submanifolds with constant mean curvature§, Amer. J. Math. 96 (1974), no. 2,
346每366.............................................................................................................53
※Submanifolds with constant mean curvature II§, Amer. J. Math. 97 (1975), no. 1,
76每100...............................................................................................................75
Contents of the Current Volume
※Curvature preserving diffeomorphisms§, Annals of Mathematics (2) 100
(1974), 121每130. .............................................................................................. 101
※Non-existence of continuous convex functions on certain Riemannian manifolds§,
Math. Ann. 207 (1974) 269每270......................................................................... 111
(with S.-Y. Cheng), ※Hypersurfaces with constant scalar curvature§, Math. Ann. 225
(1977), no. 3, 195每204. ..................................................................................... 113
(with R. Schoen and L. Simon), ※Curvature estimates for minimal hypersurfaces§,
Acta Math. 134 (1975), no. 3-4, 275每288. ........................................................... 123
(with S.-Y. Cheng), ※Maximal space-like hypersurfaces in the Lorentz-Minkowski
spaces§, Annals of Mathematics 104 (1976), no. 3, 407每419. ................................... 137
※Remarks on the group of isometries of a Riemannian manifold§, Topology 16
(1977), no. 3, 239每247. ..................................................................................... 151
(with W. H. Meeks), ※The equivariant Dehn＊s lemma and loop theorem§, Comment.
Math. Helv. 56 (1981) 225每239. ......................................................................... 161
(with R. Schoen), ※On the structure of manifolds with positive scalar curvature§,
Manuscripta Math. 28 (1979), no. 1-3, 159每183................................................... 177
(with W. H. Meeks), ※The equivariant loop theorem for three-dimensional
manifolds and a review of the existence theorems for minimal surfaces§,
Pure Appl. Math. 112 (1984) 153每163. ................................................................ 191
(with W. H. Meeks), ※Topology of three-dimensional manifolds and the embedding
problems in minimal surface theory§, Annals of Mathematics 112
(1980) 441每484. ............................................................................................... 203
(with W. H. Meeks), ※The classical Plateau problem and the topology of three-
dimensional manifolds: The embedding of the solution given by Douglas-Morrey
and an analytic proof of Dehn＊s lemma§, Topology 21 (1982) 409每442. ................... 247
(with W. H. Meeks and L. Simon), ※Embedded minimal surfaces, exotic spheres,
and manifolds with positive Ricci curvature§, Annals of Mathematics 116 (1982), 621每
659. ................................................................................................................. 281
(with R. Schoen), ※Complete three-dimensional manifolds with positive Ricci
curvature and scalar curvature§, Annals of Mathematics Studies 102 (Seminar
on Differential Geometry) 209每228, Princeton University Press, 1982..................... 321
Volume 1. Metric Geometry and Minimal Submanifolds
(with W.H. Meeks), ※The existence of embedded minimal surfaces and the problem
of uniqueness§, Math. Z. 179 (1982), 151每168..................................................... 341
(with W. H. Meeks), ※Group actions on R3§, Pure Appl. Math. 112 (1984),
167每179........................................................................................................... 359
Appendices
Photographs ..................................................................................................................... 373
Acknowledgements .......................................................................................................... 383
Contents of Volumes 2, 3, 4 and 5
Volume 2
metric Geometry and Harmonic functionS
Foreword by Shing-Tung Yau ........................................................................................... XV
Preface by the Editors ....................................................................................................... XXI
Commentary by Peter Li ............................................................................................... XXIII
Articles
(with M. Friedman), ※Homotopically trivial symmetries of Haken manifolds are
toral§, Topology 22 (1983) 179每189. ........................................................................1
(with S.-Y. Cheng), ※Complete affine hypersurfaces. I. The completeness of affine
metrics§, Comm. Pure Appl. Math. 39 (1986) 839每866. ...........................................13
(with R. Schoen), ※The structure of manifolds with positive scalar curvature§, in
Directions in Partial Differential Equations, 235每242. Madison, Wisconsin:
Academic Press, 1987. ..................................................................................................41
(with L. Z. Gao), ※The existence of negatively Ricci curved metrics on three-
manifolds§, Inventiones Mathematicae 85 (1986) 637每652........................................49
(with R. Schoen), ※Conformally flat manifolds, Kleinian groups and scalar
curvature§, Inventiones Mathematicae 92 (1988) 47每71. ...........................................65
※Uniformization of geometric structures§, Proc. Sympos. Pure Math. 48 (1988)
265每274.............................................................................................................91
※Harmonic functions on complete Riemannian manifolds§, Comm. Pure Appl.
Math. 28 (1975), 201每228. ................................................................................ 101
(with S.-Y. Cheng), ※Differential equations on Riemannian manifolds and their
geometric applications§, Comm. Pure Appl. Math. 28 (1975) 333每354..................... 129
Contents of Volumes 2, 3, 4 and 5
※Isoperimetric constants and the first eigenvalue of a compact Riemannian
manifold§, Ann. Sci. Ecole Norm. Sup. (4) 8 (1975), no. 4, 487每507. ....................... 151
※Some function-theoretic properties of complete Riemannian manifold and their
applications to geometry§, Indiana Univ. Math. J. 25 (1976), no. 7, 659每670........... 173
※Erratum to ＆Some function-theoretic properties of complete Riemannian
manifold and their applications to geometry＊§, Indiana Univ. Math. J. 31
(1982), no. 4, 607. ............................................................................................ 185
(with R. Schoen), ※Harmonic maps and the topology of stable hypersurfaces and
manifolds with non-negative Ricci curvature, Comment. Math. Helv. 51 (1976),
no. 3, 333每341.................................................................................................. 187
※A general Schwarz lemma for K.hler manifolds§, Amer. J. Math. 100 (1978), no. 1,
197每203........................................................................................................... 197
(with R. Schoen), ※On univalent harmonic maps between surfaces§, Inventiones
Mathematicae 44 (1978), no. 3, 265每278. ............................................................ 205
※On the heat kernel of a complete Riemannian manifold§, J. Math. pures et appl.
(9) 57 (1978), no. 2, 191每201. ........................................................................... 219
(with R. Schoen), ※Compact group actions and the topology of manifolds with non-
positive curvature§, Topology 18 (1979), no. 4, 361每380......................................... 231
(with R. Schoen), ※Corrections to: ＆Compact group actions and the topology of
manifolds with non-positive curvature＊§, Topology 18 (1979), no. 4, 483.................. 251
(with P. Li), ※A new conformal invariant and its applications to the Willmore
conjecture and the first eigenvalue of compact surfaces§,
Inventiones Mathematicae 69 (1982) 269每291. ...................................................... 253
(with P. Li and R. Schoen), ※On the isoperimetric inequality for minimal surfaces§,
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984) 237每244. .................................. 277
(with J. Jost), ※The strong rigidity of locally symmetric complex manifolds of rank
one and finite volume§, Math. Ann. 275 (1986) 291每304....................................... 285
(with J. Jost), ※Harmonic maps and K.hler geometry§, in Prospects in Complex
Geometry, pp. 340每370, Lecture Notes in Math. 1468, Springer, 1991. .................... 299
Volume 3. Eigenvalues and General Relativity
※Problem Section§, Annals of Mathematics Studies 102 (Seminar on Differential
Geometry), 669每706, Princeton University Press, 1982............................................ 331
Appendices
Photographs ..................................................................................................................... 369
Acknowledgements ...........................................................................................................373
Volume 3
eiGenValueS and General relatiVity
Foreword by Shing-Tung Yau .......................................................................................... XV
Preface by the Editors ...................................................................................................... XXI
Articles
(with P. Li), ※Estimates of eigenvalues of a compact Riemannian manifold, in
Geometry of the Laplace operator, pp. 205每239, Proc. Sympos. Pure Math. 36,
American Mathematical Society, 1980......................................................................1
(with R. Schoen and S. Wolpert), ※Geometric bounds on the low eigenvalues of a
compact surface: Geometry of the Laplace operator§, pp. 279每285, Proc.
Sympos. Pure Math. 36, American Mathematical Society, 1980..................................37
(with Paul C. Yang) ※Eigenvalues of the Laplacian of compact Riemann surfaces
and minimal submanifolds§, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7
(1980) 55每63......................................................................................................45
(with J. Cheeger), ※A lower bound for the heat kernel§, Comm. Pure Appl. Math.
34 (1981) 465每480..............................................................................................55
(with S.-Y. Cheng and P. Li), ※On the upper estimate of the heat kernel of a
complete Riemannian manifold§, Amer. J. Math. 103 (1981) 1021每1063. .................71
(with P. Li), ※On the Schr.dinger equation and the eigenvalue problem§, Comm.
Math. Phys. 88 (1983) 309每318. ......................................................................... 115
(with S.-Y. Cheng and P. Li), ※Heat equations on minimal submanifolds and their
applications§, Amer. J. Math. 106 (1984) 1033每1065............................................. 125
Contents of Volumes 2, 3, 4 and 5
(with I. M. Singer, B. Wong and Stephen S.-T. Yau), ※An estimate of the gap of the
first two eigenvalues in the Schr.dinger operator§, Ann. Scuola Norm. Sup.
Pisa Cl. Sci. (4) 12 (1985), 319每333. ................................................................... 159
(with P. Li), ※On the parabolic kernel of the Schr.dinger operator§, Acta Math.
156 (1986) 153每201.......................................................................................... 175
(with Y. Y. Lu), ※Eigenvalues of the Laplacian through boundary integral equations§,
SIAM J. Matrix Anal. Appl. 12 (1991) 597每609. ................................................... 225
(with R. Schoen), ※Positivity of the total mass of a general space-time§, Phys. Rev.
Lett. 43 (1979), no. 20, 1457每1459..................................................................... 239
(with R. Schoen), ※Existence of incompressible minimal surfaces and the topology
of three-dimensional manifolds with nonnegative scalar curvature§, Annals of
Mathematics (2) 110 (1979) 127每142................................................................... 243
(with R. Schoen), ※On the proof of the positive mass conjecture in general
relativity§, Comm. Math. Phys. 65 (1979), no. 1, 45每76. ........................................ 259
※The total mass and the topology of an asymptotically flat space-time§, in The
Chern Symposium 1979, pp. 255每259. Springer, 1980............................................ 291
(with R. Schoen, ※The energy and the linear momentum of space-times in general
relativity§, Comm. Math. Phys. 79 (1981) 47每51. .................................................. 297
(with R. Schoen), ※Proof of the positive mass theorem, II§, Comm. Math. Phys. 79
(1981) 231每260. ............................................................................................... 303
(with R. Schoen), ※Proof that the Bondi mass is positive§, Phys. Rev. Lett. 48
(1982) 369每371. ............................................................................................... 333
(with R. Schoen), ※The existence of a black hole due to condensation of matter§,
Comm. Math. Phys. 90 (1983) 575每579. .............................................................. 337
(with D. Christodoulou), ※Some remarks on the quasi-local mass§, 9每14, Contemp.
Math. 71, American Mathematical Society, 1988........................................................343
(with J. Smoller, A. Wasserman and B. McLeod), ※Smooth static solutions of the
Einstein/Yang-Mills equations§, Comm. Math. Phys. 143 (1991) 115每147................ 349
Volume 4. K.hler Geometry I
Appendices
Photographs ......................................................................................................................383
Acknowledgements ............................................................................................................389
Volume 4
K.Hler Geometry i
Foreword by Shing-Tung Yau .......................................................................................... XIII
Preface by the Editors .......................................................................................................XIX
Commentary by Duong H. Phong ................................................................................... XXI
Commentary by Ngaiming Mok .................................................................................... XXV
Articles
※The role of partial differential equations in differential geometry§, in Proceedings
of the International Congress of Mathematicians, 237每250. Helsinki: Acad.
Sci. Fennica, 1980. ................................................................................................1
(with J.-P. Bourguignon), ※Sur les m谷triques riemanniennes 芍 courbure de Ricci
nulle sur le quotient d＊une surface K3§, C. R. Acad. Sci. Paris S谷r. A-B 277
(1973), A1175每A1177. ........................................................................................15
(with S.-Y. Cheng), ※On the regularity of the solution of the n-dimensional
Minkowski problem§, Comm. Pure Appl. Math. 29 (1976), no. 5, 495每516................19
※Intrinsic measures of compact complex manifolds§, Math. Ann. 212 (1975),
317每329.............................................................................................................41
(with Yum-Tong Siu), ※On the structure of complete simply-connected K.hler
manifolds with nonpositive curvature§, Proc. Nat. Acad. Sci. U.S.A. 73 (1976),
no. 4, p. 1008...............................................................................................................55
※Parallelizable manifolds without complex structure§, Topology 15 (1976), no. 1,
51每53. ...............................................................................................................57
(with S.-Y. Cheng), ※On the regularity of the Monge每Amp豕re equation§, Comm.
Pure Appl. Math. 30 (1977), no. 1, 41每68.....................................................................61
Contents of Volumes 2, 3, 4 and 5
※Calabi＊s conjecture and some new results in algebraic geometry§, Proc. Nat. Acad.
Sci. U.S.A. 74 (1977), no. 5, 1798每1799................................................................89
(with Y.-T. Siu), ※Complete K.hler manifolds with nonpositive curvature of faster
than quadratic decay§, Annals of Mathematics (2) 105 (1977), no. 2, 225每264. ...........91
※On the Ricci curvature of a compact K.hler manifold and the complex Monge-
Amp谷re equation. I§, Comm. Pure Appl. Math. 31 (1978), no. 3, 339每411. .............. 131
※M谷triques de K.hler-Einstein sur les vari谷t谷s ouvert谷s§, Ast谷risque 58 (1978)
163-167. .......................................................................................................... 205
(with S.-Y. Cheng), ※On the existence of a complete K.hler metric on noncompact
complex manifolds and the regularity of Fefferman＊s equation§, Comm. Pure
Appl. Math. 33 (1980) 507每544. ......................................................................... 211
(with Y.-T. Siu), ※Compact K.hler manifolds of positive bisectional curvature§,
Inventiones Mathematicae 59 (1980) 189每204. ...................................................... 249
(with N. Mok and Y.-T. Siu), ※The Poincar谷-Lelong equation on complete K.hler
manifolds§, Compositio Math. 44 (1981) 183每218................................................. 265
(with S.-Y. Cheng), ※The real Monge每Amp豕re equation and affine flat structures§,
in Proceedings of the 1980 Beijing Symposium on Differential Geometry and
Differential Equations, 339每370. Beijing: Science Press, 1982.................................. 301
(with Y.-T. Siu), ※Compactification of negatively curved complete K.hler manifolds
of finite volume§, Annals of Mathematics Studies 102 (Seminar on Differential
Geometry), 363每380, Princeton University Press, 1982............................................ 333
(with N. Mok), ※Completeness of the K.hler-Einstein metric on bounded domains
and the characterization of domains of holomorphy by curvature conditions§,
Proc. Sympos. Pure Math. 39, Part 1 (1983), 41每59. ............................................... 351
Appendices
Photographs ......................................................................................................................371
Acknowledgements ............................................................................................................375
Volume 5. K.hler Geometry II
Volume 5
K.Hler Geometry ii
Foreword by Shing-Tung Yau .......................................................................................... XIII
Preface by the Editors .......................................................................................................XIX
Articles
(with K. Uhlenbeck), ※On the existence of Hermitian-Yang-Mills connections in
stable vector bundles§, Comm. Pure Appl. Math. 39 (1986), supplement,
S257每S293. ..........................................................................................................1
(with J. Jost), ※A strong rigidity theorem for a certain class of compact complex
analytic surfaces§, Math. Ann. 271 (1985) 143每152.................................................39
(with S. Y. Cheng), ※Inequality between Chern numbers of singular K.hler surfaces
and characterization of orbit space of discrete group of SU (2, 1)§, Contemp.
Math. 49 (1986), 31每44.......................................................................................49
※Nonlinear analysis in geometry§, Enseign. Math. (2) 33 (1987) no. 1-2, 109每158. ...........63
(with J. Li), ※Hermitian-Yang-Mills Connection on Non-K.hler Manifolds§, in
Mathematical Aspects of String Theory, 560每573, World Scientific, 1987.
DOI: 10.1142/9789812798411_0027.......................................................................113
(with G. Tian), ※Existence of K.hler-Einstein metrics on complete K.hler manifolds
and their applications to algebraic geometry§, in Mathematical Aspects of
String Theory, 574每628, World Scientific, 1987.
DOI: 10.1142/9789812798411_0028................................................................. 127
(with G. Tian), ※Three-dimensional algebraic manifolds with C1 = 0 and 聿 = 每6§,
in Mathematical Aspects of String Theory, 543每559, World Scientific, 1987.
DOI: 10.1142/9789812798411_0026................................................................. 183
(with G. Tian), ※K.hler-Einstein metrics on complex surfaces with C1 > 0§, Comm.
Math. Phys. 112 (1987) 175每203......................................................................... 201
(with K. Uhlenbeck), ※A note on our previous paper: ＆On the existence of Hermitian
Yang-Mills connections in stable vector bundles＊§, [Comm. Pure Appl. Math.
39 (1986), S257每S293], Comm. Pure Appl. Math. 42 (1989) 703每707. ................... 231
Contents of Volumes 2, 3, 4 and 5
(with B. R. Green, A. Shapere and C. Vafa), ※Stringy cosmic strings and non-
compact Calabi-Yau manifolds§, Nuclear Phys. B 337 (1990), no. 1, 1每36................ 237
(with J. Li and F. Zheng), ※A simple proof of Bogomolov＊s theorem on class .II0
surfaces with b2 = 01§, Illinois J. Math. 34 (1990) 217每220..................................... 273
(with S.-Y. Lu), ※Holomorphic curves in surfaces of general type§, Proc. Nat. Acad.
Sci. U.S.A. 87 (1990) 80每82. .............................................................................. 277
(with G. Tian), ※Complete K.hler manifolds with zero Ricci curvature. I§, J. Amer.
Math. Soc. 3 (1990) 579每609.............................................................................. 281
(with B. R. Greene and S.-S. Roane), ※Geometric singularities and spectra of
Landau-Ginzburg models§, Comm. Math. Phys. 142 (1991) 245每259...................... 313
(with F. Zheng), ※On projective manifolds covered by space C.§, in International
Symposium in Memory of Hua Loo Keng, Vol. II (Beijing, 1988), 323每332,
Springer, 1991................................................................................................... 329
(with F. Zheng), ※Negatively 1/4-pinched Riemannian metric on a compact K.hler
manifold§, Inventiones Mathematicae 103 (1991) 527每535. .................................... 339
(with G. Tian), ※Complete K.hler manifolds with zero Ricci curvature. II§,
Inventiones Mathematicae 106 (1991) 27每60......................................................... 349
Appendices
Curriculum Vitae of Shing-Tung Yau ...............................................................................383
List of Former Students .....................................................................................................387
List of Publications by Shing-Tung Yau, 1970每1991 ........................................................389
Acknowledgements ............................................................................................................397
