Differential Geometry and Related Topics: Proceedings of the International Conference and Modern Mathematics and the International Symposium on Differential Geometry

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. 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 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. Book jacket Around 100 international mathematicians participated in the International Conference on Modern Mathematics and the International Symposium on Differential Geometry in 2001. This volume of proceedings covers a broad spectrum of topics in differential geometry and advanced mathematics.