若干演化为球面的曲率流 英文版
出版时间： 2018年版
内容简介
本书系统总结了作者在快速发展的几何流领域取得的新的、有趣的及重要的研究成果。著作分为8章,内容涉及欧氏空间中的依赖平均曲率的一般函子流和保混合体积的一般函子的幂次流及子流形的带外力场的平均曲率流,和双曲空间中的幂平均曲率流、依赖平均曲率的一般函子流和保体积的主曲率的初等函子的幂次流。
目录
《博士后文库》序言
Preface
Chapter 1 Preliminary 1
1.1 Notations 1
1.2 Some useful properties 4
1.3 Graphical submanifolds 7
1.4 Interior Holder estimates 10
Chapter 2 HΒ-flow for h-convex Hypersurfaces in 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
Chapter 3 HΒ-flow for Pinched Hypersurfaces in 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
Chapter 4 Volume-preserving flow in 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
Chapter 5 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
Chapter 6 flow in 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
Chapter 7 Mixed Volume Preserving 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 (F) 164
7.5 Long-time existence 169
7.6 Exponential convergence to the sphere 175
Chapter 8 Forced MCF of Submanifolds in 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