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丘成桐數(shù)學(xué)論文選集(1971—1991 英文版)

丘成桐數(shù)學(xué)論文選集(1971—1991 英文版)

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作 者: 曹懷東,李駿,[美]孫理察
出版社: 清華大學(xué)出版社
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標(biāo) 簽: 暫缺

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ISBN: 9787302664727 出版時(shí)間: 2024-06-01 包裝: 精裝
開本: 16開 頁(yè)數(shù): 字?jǐn)?shù):  

內(nèi)容簡(jiǎn)介

  丘成桐是當(dāng)代最杰出的數(shù)學(xué)家之一,因其在微分幾何領(lǐng)域的工作而獲得了許多榮譽(yù),其中包括數(shù)學(xué)界最高榮譽(yù)——菲爾茲獎(jiǎng)。丘成桐也因其在代數(shù)和凱勒幾何、廣義相對(duì)論及弦理論等方面的工作而聞名,他在這些研究領(lǐng)域的建立和發(fā)展過(guò)程中產(chǎn)生了巨大的影響。本書收錄了丘成桐自1971年至1991年已發(fā)表的部分?jǐn)?shù)學(xué)論文——這一時(shí)期他在包括幾何分析、凱勒幾何和廣義相對(duì)論在內(nèi)的眾多學(xué)科中取得了突破性的成就。本書按照主題領(lǐng)域組織內(nèi)容,包括度量幾何與極小子流形、度量幾何與調(diào)和函數(shù)、本征值與廣義相對(duì)論,以及凱勒幾何。書中還收錄了相關(guān)領(lǐng)域?qū)<业脑u(píng)論和反映書中所討論的思想發(fā)展過(guò)程的回顧。

作者簡(jiǎn)介

  曹懷東,美國(guó)里海(Lehigh)大學(xué)數(shù)學(xué)系講座教授,清華大學(xué)兼職教授。主要從事的研究領(lǐng)域是微分幾何學(xué)與非線性偏微分方程,涉及Kahler-Ricci流、數(shù)學(xué)物理等眾多方面。李駿,基礎(chǔ)數(shù)學(xué)代數(shù)幾何學(xué)家,中國(guó)科學(xué)院院士,復(fù)旦大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授,復(fù)旦大學(xué)上海數(shù)學(xué)中心首席教授,上海數(shù)學(xué)與交叉學(xué)科研究院院長(zhǎng),斯坦福大學(xué)終身教授。主要從事代數(shù)幾何??臻g方向的研究。孫理察(Richard Schoen),美國(guó)數(shù)學(xué)家,沃爾夫數(shù)學(xué)獎(jiǎng)獲得者,美國(guó)國(guó)家科學(xué)院院士,美國(guó)藝術(shù)與科學(xué)院院士,美國(guó)科學(xué)促進(jìn)會(huì)會(huì)士,美國(guó)數(shù)學(xué)學(xué)會(huì)會(huì)士,斯坦福大學(xué)名譽(yù)教授。主要研究微分幾何和幾何分析等數(shù)學(xué)問(wèn)題。

圖書目錄

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) 579–585  1 
(with H Lawson), “Compact manifolds of nonpositive curvature”, J Differential 
Geom 7 (1972), 211–2289 
“Some global theorems on non-complete surfaces”, Comment Math Helv 48 
(1973), 177–187 27 
(with H Lawson), “Scalar curvature, non-abelian group actions, and the degree of 
symmetry of exotic spheres”, Comment Math Helv 49 (1974), 232–24439 
“Submanifolds with constant mean curvature”, Amer J Math 96 (1974), no 2, 
346–36653 
“Submanifolds with constant mean curvature II”, Amer J Math 97 (1975), no 1, 
76–10075 
 
Contents of the Current Volume 
“Curvature preserving diffeomorphisms”, Annals of Mathematics (2) 100 
(1974), 121–130  101 
“Non-existence of continuous convex functions on certain Riemannian manifolds”, 
Math Ann 207 (1974) 269–270 111 
(with S-Y Cheng), “Hypersurfaces with constant scalar curvature”, Math Ann 225 
(1977), no 3, 195–204  113 
(with R Schoen and L Simon), “Curvature estimates for minimal hypersurfaces”, 
Acta Math 134 (1975), no 3-4, 275–288  123 
(with S-Y Cheng), “Maximal space-like hypersurfaces in the Lorentz-Minkowski 
spaces”, Annals of Mathematics 104 (1976), no 3, 407–419  137 
“Remarks on the group of isometries of a Riemannian manifold”, Topology 16 
(1977), no 3, 239–247  151 
(with W H Meeks), “The equivariant Dehn’s lemma and loop theorem”, Comment 
Math Helv 56 (1981) 225–239  161 
(with R Schoen), “On the structure of manifolds with positive scalar curvature”, 
Manuscripta Math 28 (1979), no 1-3, 159–183 177 
(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) 153–163  191 
(with W H Meeks), “Topology of three-dimensional manifolds and the embedding 
problems in minimal surface theory”, Annals of Mathematics 112 
(1980) 441–484  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) 409–442  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– 
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) 209–228, Princeton University Press, 1982 321 
 
Volume 1 Metric Geometry and Minimal Submanifolds 
(with WH Meeks), “The existence of embedded minimal surfaces and the problem 
of uniqueness”, Math Z 179 (1982), 151–168 341 
(with W H Meeks), “Group actions on R3”, Pure Appl Math 112 (1984), 
167–179 359 
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) 179–189 1 
(with S-Y Cheng), “Complete affine hypersurfaces I The completeness of affine 
metrics”, Comm Pure Appl Math 39 (1986) 839–866 13 
(with R Schoen), “The structure of manifolds with positive scalar curvature”, in 
Directions in Partial Differential Equations, 235–242 Madison, Wisconsin: 
Academic Press, 1987 41 
(with L Z Gao), “The existence of negatively Ricci curved metrics on three- 
manifolds”, Inventiones Mathematicae 85 (1986) 637–65249 
(with R Schoen), “Conformally flat manifolds, Kleinian groups and scalar 
curvature”, Inventiones Mathematicae 92 (1988) 47–71 65 
“Uniformization of geometric structures”, Proc Sympos Pure Math 48 (1988) 
265–27491 
“Harmonic functions on complete Riemannian manifolds”, Comm Pure Appl 
Math 28 (1975), 201–228  101 
(with S-Y Cheng), “Differential equations on Riemannian manifolds and their 
geometric applications”, Comm Pure Appl Math 28 (1975) 333–354 129 
 
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, 487–507  151 
“Some function-theoretic properties of complete Riemannian manifold and their 
applications to geometry”, Indiana Univ Math J 25 (1976), no 7, 659–670 173 
“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, 333–341 187 
“A general Schwarz lemma for Khler manifolds”, Amer J Math 100 (1978), no 1, 
197–203 197 
(with R Schoen), “On univalent harmonic maps between surfaces”, Inventiones 
Mathematicae 44 (1978), no 3, 265–278  205 
“On the heat kernel of a complete Riemannian manifold”, J Math pures et appl 
(9) 57 (1978), no 2, 191–201  219 
(with R Schoen), “Compact group actions and the topology of manifolds with non- 
positive curvature”, Topology 18 (1979), no 4, 361–380 231 
(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) 269–291  253 
(with P Li and R Schoen), “On the isoperimetric inequality for minimal surfaces”, 
Ann Scuola Norm Sup Pisa Cl Sci (4) 11 (1984) 237–244  277 
(with J Jost), “The strong rigidity of locally symmetric complex manifolds of rank 
one and finite volume”, Math Ann 275 (1986) 291–304 285 
(with J Jost), “Harmonic maps and Khler geometry”, in Prospects in Complex 
Geometry, pp 340–370, 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), 669–706, 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 205–239, Proc Sympos Pure Math 36, 
American Mathematical Society, 19801 
(with R Schoen and S Wolpert), “Geometric bounds on the low eigenvalues of a 
compact surface: Geometry of the Laplace operator”, pp 279–285, Proc 
Sympos Pure Math 36, American Mathematical Society, 198037 
(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) 55–6345 
(with J Cheeger), “A lower bound for the heat kernel”, Comm Pure Appl Math 
34 (1981) 465–48055 
(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) 1021–1063 71 
(with P Li), “On the Schrdinger equation and the eigenvalue problem”, Comm 
Math Phys 88 (1983) 309–318  115 
(with S-Y Cheng and P Li), “Heat equations on minimal submanifolds and their 
applications”, Amer J Math 106 (1984) 1033–1065 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 Schrdinger operator”, Ann Scuola Norm Sup 
Pisa Cl Sci (4) 12 (1985), 319–333  159 
(with P Li), “On the parabolic kernel of the Schrdinger operator”, Acta Math 
156 (1986) 153–201 175 
(with Y Y Lu), “Eigenvalues of the Laplacian through boundary integral equations”, 
SIAM J Matrix Anal Appl 12 (1991) 597–609  225 
(with R Schoen), “Positivity of the total mass of a general space-time”, Phys Rev 
Lett 43 (1979), no 20, 1457–1459 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) 127–142 243 
(with R Schoen), “On the proof of the positive mass conjecture in general 
relativity”, Comm Math Phys 65 (1979), no 1, 45–76  259 
“The total mass and the topology of an asymptotically flat space-time”, in The 
Chern Symposium 1979, pp 255–259 Springer, 1980 291 
(with R Schoen, “The energy and the linear momentum of space-times in general 
relativity”, Comm Math Phys 79 (1981) 47–51  297 
(with R Schoen), “Proof of the positive mass theorem, II”, Comm Math Phys 79 
(1981) 231–260  303 
(with R Schoen), “Proof that the Bondi mass is positive”, Phys Rev Lett 48 
(1982) 369–371  333 
(with R Schoen), “The existence of a black hole due to condensation of matter”, 
Comm Math Phys 90 (1983) 575–579  337 
(with D Christodoulou), “Some remarks on the quasi-local mass”, 9–14, Contemp 
Math 71, American Mathematical Society, 1988343 
(with J Smoller, A Wasserman and B McLeod), “Smooth static solutions of the 
Einstein/Yang-Mills equations”, Comm Math Phys 143 (1991) 115–147 349 
 
Volume 4 Khler Geometry I 
Appendices 
Photographs 383 
Acknowledgements 389 
Volume 4 
KHler 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, 237–250 Helsinki: Acad 
Sci Fennica, 1980 1 
(with J-P Bourguignon), “Sur les métriques riemanniennes á courbure de Ricci 
nulle sur le quotient d’une surface K3”, C R Acad Sci Paris Sér A-B 277 
(1973), A1175–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, 495–51619 
“Intrinsic measures of compact complex manifolds”, Math Ann 212 (1975), 
317–32941 
(with Yum-Tong Siu), “On the structure of complete simply-connected Khler 
manifolds with nonpositive curvature”, Proc Nat Acad Sci USA 73 (1976), 
no 4, p 100855 
“Parallelizable manifolds without complex structure”, Topology 15 (1976), no 1, 
51–53 57 
(with S-Y Cheng), “On the regularity of the Monge–Ampère equation”, Comm 
Pure Appl Math 30 (1977), no 1, 41–6861 
 
Contents of Volumes 2, 3, 4 and 5 
“Calabi’s conjecture and some new results in algebraic geometry”, Proc Nat Acad 
Sci USA 74 (1977), no 5, 1798–179989 
(with Y-T Siu), “Complete Khler manifolds with nonpositive curvature of faster 
than quadratic decay”, Annals of Mathematics (2) 105 (1977), no 2, 225–264 91 
“On the Ricci curvature of a compact Khler manifold and the complex Monge- 
Ampére equation I”, Comm Pure Appl Math 31 (1978), no 3, 339–411  131 
“Métriques de Khler-Einstein sur les variétés ouvertés”, Astérisque 58 (1978) 
163-167  205 
(with S-Y Cheng), “On the existence of a complete Khler metric on noncompact 
complex manifolds and the regularity of Fefferman’s equation”, Comm Pure 
Appl Math 33 (1980) 507–544  211 
(with Y-T Siu), “Compact Khler manifolds of positive bisectional curvature”, 
Inventiones Mathematicae 59 (1980) 189–204  249 
(with N Mok and Y-T Siu), “The Poincaré-Lelong equation on complete Khler 
manifolds”, Compositio Math 44 (1981) 183–218 265 
(with S-Y Cheng), “The real Monge–Ampère equation and affine flat structures”, 
in Proceedings of the 1980 Beijing Symposium on Differential Geometry and 
Differential Equations, 339–370 Beijing: Science Press, 1982 301 
(with Y-T Siu), “Compactification of negatively curved complete Khler manifolds 
of finite volume”, Annals of Mathematics Studies 102 (Seminar on Differential 
Geometry), 363–380, Princeton University Press, 1982 333 
(with N Mok), “Completeness of the Khler-Einstein metric on bounded domains 
and the characterization of domains of holomorphy by curvature conditions”, 
Proc Sympos Pure Math 39, Part 1 (1983), 41–59  351 
Appendices 
Photographs 371 
Acknowledgements 375 
 
Volume 5 Khler Geometry II 
Volume 5 
KHler 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–S293 1 
(with J Jost), “A strong rigidity theorem for a certain class of compact complex 
analytic surfaces”, Math Ann 271 (1985) 143–15239 
(with S Y Cheng), “Inequality between Chern numbers of singular Khler surfaces 
and characterization of orbit space of discrete group of SU (2, 1)”, Contemp 
Math 49 (1986), 31–4449 
“Nonlinear analysis in geometry”, Enseign Math (2) 33 (1987) no 1-2, 109–158 63 
(with J Li), “Hermitian-Yang-Mills Connection on Non-Khler Manifolds”, in 
Mathematical Aspects of String Theory, 560–573, World Scientific, 1987 
DOI: 101142/9789812798411_0027113 
(with G Tian), “Existence of Khler-Einstein metrics on complete Khler manifolds 
and their applications to algebraic geometry”, in Mathematical Aspects of 
String Theory, 574–628, World Scientific, 1987 
DOI: 101142/9789812798411_0028 127 
(with G Tian), “Three-dimensional algebraic manifolds with C1 = 0 and χ = –6”, 
in Mathematical Aspects of String Theory, 543–559, World Scientific, 1987 
DOI: 101142/9789812798411_0026 183 
(with G Tian), “Khler-Einstein metrics on complex surfaces with C1 > 0”, Comm 
Math Phys 112 (1987) 175–203 201 
(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–S293], Comm Pure Appl Math 42 (1989) 703–707  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, 1–36 237 
(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) 217–220 273 
(with S-Y Lu), “Holomorphic curves in surfaces of general type”, Proc Nat Acad 
Sci USA 87 (1990) 80–82  277 
(with G Tian), “Complete Khler manifolds with zero Ricci curvature I”, J Amer 
Math Soc 3 (1990) 579–609 281 
(with B R Greene and S-S Roane), “Geometric singularities and spectra of 
Landau-Ginzburg models”, Comm Math Phys 142 (1991) 245–259 313 
(with F Zheng), “On projective manifolds covered by space C”, in International 
Symposium in Memory of Hua Loo Keng, Vol II (Beijing, 1988), 323–332, 
Springer, 1991 329 
(with F Zheng), “Negatively 1/4-pinched Riemannian metric on a compact Khler 
manifold”, Inventiones Mathematicae 103 (1991) 527–535  339 
(with G Tian), “Complete Khler manifolds with zero Ricci curvature II”, 
Inventiones Mathematicae 106 (1991) 27–60 349 
Appendices 
Curriculum Vitae of Shing-Tung Yau 383 
List of Former Students 387 
List of Publications by Shing-Tung Yau, 1970–1991 389 
Acknowledgements 397 
 

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