The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China. Around 100 mathematicians from China, France, Japan, Singapore and the United States participated. The proceedings cover a broad spectrum of advanced topics in mathematics, especially in differential geometry, such as some problems of common interest in harmonic maps, submanifolds, the Yang-Mills field and the geometric theory of solitons.
Author(s): Chaohao G. (ed.), Hesheng H. (ed.), Tatsien L. (ed.)
Year: 2003
Language: English
Commentary: (add ocr)
Pages: 291
Contents......Page 8
Preface......Page 6
S0 Introduction......Page 11
S2 The isothermic surfaces in S3(1)......Page 15
S3 The Backlund transformations of (2.17) and (2.18)......Page 22
References......Page 24
S1. INTRODUCTION......Page 26
S2. ENERGY INEQUALITY BOCHNER TYPE INEQUALITY MONOTONICITY FORMULA AND PARTIAL REGULARITY THEOREM FOR YANG-MLLLS FLOW......Page 28
S3. THE ESTIMATES OF HIGHER DERIVATIVES OF CURVATURES OF YANG-MILLS FLOW......Page 33
S4. PROOF OF MAIN THEOREM......Page 35
S5. APPENDIX......Page 45
REFERENCES......Page 48
1.INTRODUCTION......Page 49
2. SYMBOLS AND SOME LEMMAS......Page 50
3.THE PROOF OF THEOREM 1......Page 55
REFERENCES......Page 57
2. PRELIMINARIES......Page 58
3. COMPLETE HYPERSURFACES......Page 61
4. COMPLETE SUBMANIFOLDS......Page 68
REFERENCES......Page 72
On mathematical ship lofting......Page 74
References......Page 76
1. Introduction......Page 78
2. Hermite Spectral Method and Lagaerre spectral method......Page 79
3. Jacobi Spectral Method......Page 84
4. Rational Spectral Method......Page 90
References......Page 99
1 Introduction......Page 101
2 Preliminaries......Page 102
3 Non-umbilically isometric immersions of space forms......Page 106
4 Darboux transformation......Page 110
5 The construction of local isometric immersions derived from a trivial solution......Page 113
Acknowledgments......Page 115
References......Page 116
S1. Introduction......Page 117
S2. Kazdan-Warner condition......Page 119
S3. Existence of solutions......Page 126
S4. Preliminaries......Page 134
S5. Main steps of proofs......Page 137
References......Page 142
2. Periodic surfaces of revolution......Page 145
3. Closed curves......Page 148
4. Bezier curves......Page 153
References......Page 156
1. Almost complex manifolds......Page 157
2. Canonical connections for almost Hermitian manifolds......Page 159
3. Almost complex submanifolds......Page 161
4. Conformal changes......Page 163
5. Differential geometric criterion for hyperbolicity......Page 164
References......Page 166
2. Equivariant Cohomology......Page 167
3. Kobayashi Lemma......Page 169
4. The Thorn Isommorphism of the Normal Bundle......Page 171
References......Page 174
1 Introduction......Page 176
2 The Fundamental Equation for a Horizontally Conformal Map......Page 178
3 An Extension of Baird and Eells' Result......Page 180
4 F-harmonicity of Horizontally Conformal Maps......Page 181
References......Page 182
1. Introduction......Page 184
2. Carnot Spaces......Page 188
3. Asymptotic Behavior of Proper Harmonic Maps......Page 195
References......Page 212
1. Introduction......Page 214
2. Operators on O*(M) and harmonic cohomology group......Page 215
3. Harmonic cohomology group of nilmanifolds......Page 218
4. Examples......Page 221
References......Page 225
1. Introduction......Page 226
2. Model surfaces......Page 228
3. Generalized Alexandrov Toponogov Comparison Theorems......Page 230
4. Maximal diameter theorem......Page 233
References......Page 235
S1. Preliminary......Page 237
S2. Yang-Mills connections over Kahler manifolds......Page 238
S3. Yang-Mills connections over strongly pseudoconvex CR manifolds......Page 239
S4. Symplectic manifolds......Page 240
S5. Yang-Mills connections over symplectic manifolds......Page 241
REFERENCES......Page 245
1. Three classical integrable systems......Page 247
2. Schrodinger-like systems associated with Hermitian symmetric Lie algebras......Page 248
3. Gauge equivalence......Page 250
4. The correspondence between Heisenberg model and nonlinear Schrodinger equation with (quasi)-periodic boundary condition......Page 252
5. Concluding remarks......Page 255
References......Page 257
1. Introduction......Page 260
2. Existence and Uniqueness......Page 261
3. An Algorithm to Compute the Hensel Lift......Page 264
References......Page 266
I Application of coupling method to estimate the first eigenvalue......Page 267
II w24 quantum fields and polymer measures......Page 269
III Sketch of the Main Proof of I......Page 271
REFERENCES......Page 272
1. Introduction......Page 274
2. The construction of harmonic maps of finite energy......Page 275
3. Some properties of the harmonic maps......Page 277
4. The proof of the theorem......Page 279
References......Page 280
Interesting properties of the sets: N2{12 22 32 ...] N3[13 23 33...] and N4[14 24 34...]......Page 282
References......Page 286
List of participants......Page 289
