作者：郭顺滋
页数：208
出版社：科学出版社
出版日期：2018
ISBN：9787030568915
电子书格式：pdf/epub/txt
内容简介
郭顺滋著的《若干演化为球面的曲率流(英文版)/博士后文库》中课题属微分几何学的研究热点。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
Contents
《博士后文库》序言
Preface
Chapter 1 Preliminary
1.1 Notations
1.2 Some useful properties
1.3 Graphical submanifolds
1.4 Interior Holder estimates
Chapter 2 HΒ-flow for h-convex Hypersurfaces in
2.1 Introduction and main results
2.2 Short-time existence and evolution equations
2.3 Preserving h-convex
2.4 Long-time existence
2.5 Contraction to a point
Chapter 3 HΒ-flow for Pinched Hypersurfaces in
3.1 Introduction
3.2 Preserving pinching of curvature
3.3 The pinching estimate
3.4 The normalized equations
3.5 Convergence to a unit geodesic sphere
3.6 Exponential convergence
Chapter 4 Volume-preserving flow in
4.1 Introduction
4.2 Short-time existence and evolution equations
4.3 Preserving pinching
4.4 Upper bound on F
4.5 Long-time existence
4.6 Exponential convergence to a geodesic sphere
Chapter 5 flow in Rn+1
5.1 Introduction and main results
5.2 Short-time existence and evolution equations
5.3 Long-time existence
5.4 Preserving convexity
Chapter 6 flow in
6.1 Introduction and main results
6.2 Short-time existence and evolution equations
6.3 Preserving h-convex
6.4 Long-time existence
6.5 Contraction to a point
Chapter 7 Mixed Volume Preserving flow in Rn+1
7.1 Introduction and main results
7.2 Short-time existence and evolution equations
7.3 Preserving pinching
7.4 Upper bound on (F)
7.5 Long-time existence
7.6 Exponential convergence to the sphere
Chapter 8 Forced MCF of Submanifolds in
8.1 Introduction
8.2 Evolution equations
8.3 Relationship with the mean curvature flow
8.4 Asymptotic behavior of submanifolds
Bibliography
编后记
《博士后文库》序言
Preface
Chapter 1 Preliminary
1.1 Notations
1.2 Some useful properties
1.3 Graphical submanifolds
1.4 Interior Holder estimates
Chapter 2 HΒ-flow for h-convex Hypersurfaces in
2.1 Introduction and main results
2.2 Short-time existence and evolution equations
2.3 Preserving h-convex
2.4 Long-time existence
2.5 Contraction to a point
Chapter 3 HΒ-flow for Pinched Hypersurfaces in
3.1 Introduction
3.2 Preserving pinching of curvature
3.3 The pinching estimate
3.4 The normalized equations
3.5 Convergence to a unit geodesic sphere
3.6 Exponential convergence
Chapter 4 Volume-preserving flow in
4.1 Introduction
4.2 Short-time existence and evolution equations
4.3 Preserving pinching
4.4 Upper bound on F
4.5 Long-time existence
4.6 Exponential convergence to a geodesic sphere
Chapter 5 flow in Rn+1
5.1 Introduction and main results
5.2 Short-time existence and evolution equations
5.3 Long-time existence
5.4 Preserving convexity
Chapter 6 flow in
6.1 Introduction and main results
6.2 Short-time existence and evolution equations
6.3 Preserving h-convex
6.4 Long-time existence
6.5 Contraction to a point
Chapter 7 Mixed Volume Preserving flow in Rn+1
7.1 Introduction and main results
7.2 Short-time existence and evolution equations
7.3 Preserving pinching
7.4 Upper bound on (F)
7.5 Long-time existence
7.6 Exponential convergence to the sphere
Chapter 8 Forced MCF of Submanifolds in
8.1 Introduction
8.2 Evolution equations
8.3 Relationship with the mean curvature flow
8.4 Asymptotic behavior of submanifolds
Bibliography
编后记
