若干演化为球面的曲率流PDF电子书下载

Chapter1 Preliminary 1

1.1 Notations 1

1.2 Some useful properties 4

1.3 Graphical submanifolds 7

1.4 Interior Holder estimates 10

Chapter2 Hβ-flow for h-convex Hypersurfaces in H n k＋1 13

2.1 Introduction and main results 13

2.2 Short-time existence and evolution equations 16

2.3 Preserving h-convex 22

2.4 Long-time existence 27

2.5 Contraction to a point 32

Chapter3 Hβ-flow for Pinched Hypersurfaces in H n k＋1 34

3.1 Introduction 34

3.2 Preserving pinching of curvature 38

3.3 The pinching estimate 47

3.4 The normalized equations 51

3.5 Convergence to a unit geodesic sphere 55

3.6 Exponential convergence 63

Chapter4 Volume-preserving Hβ m-flow in H n k＋1 66

4.1 Introduction 66

4.2 Short-time existence and evolution equations 71

4.3 Preserving pinching 78

4.4 Upper bound on F 84

4.5 Long-time existence 93

4.6 Exponential convergence to a geodesic sphere 103

Chapter5 φ（H）-flow in Rn＋1 107

5.1 Introduction and main results 107

5.2 Short-time existence and evolution equations 111

5.3 Long-time existence 115

5.4 Preserving convexity 118

Chapter6 φ（H）-flow in H n k＋1 125

6.1 Introduction and main results 125

6.2 Short-time existence and evolution equations 128

6.3 Preserving h-convex 133

6.4 Long-time existence 139

6.5 Contraction to a point 145

Chapter7 Mixed Volume Preserving Fβ-flow in Rn＋1 146

7.1 Introduction and main results 146

7.2 Short-time existence and evolution equations 151

7.3 Preserving pinching 155

7.4 Upper bound on φ（F） 164

7.5 Long-time existence 169

7.6 Exponential convergence to the sphere 175

Chapter8 Forced MCF of Submanifolds in Rn＋p 184

8.1 Introduction 184

8.2 Evolution equations 189

8.3 Relationship with the mean curvature flow 191

8.4 Asymptotic behavior of submanifolds 194

Bibliography 201

编后记 209