中文题名: | 各阶平均曲率流问题研究 |
姓名: | |
保密级别: | 公开 |
论文语种: | 中文 |
学科代码: | 070101 |
学科专业: | |
学生类型: | 硕士 |
学位: | 理学硕士 |
学位类型: | |
学位年度: | 2020 |
校区: | |
学院: | |
研究方向: | 微分几何 |
第一导师姓名: | |
第一导师单位: | |
提交日期: | 2020-06-24 |
答辩日期: | 2020-06-24 |
外文题名: | Research on the mean curvature flow problem of every order |
中文关键词: | |
外文关键词: | Mean curvature flow ; Mean curvature of each order ; The second fundamental form ; The evolution equations. |
中文摘要: |
本文主要简单叙述了平均曲率流的一些经典结果,并拓展研究了紧致无边的黎曼流形在给定条件下,各阶平均曲率流解的存在性及演化方程.本文内容分为三章.在第一章中,是关于平均曲率流研究背景的介绍,按照曲面及余维数的分类,给了平均曲率流的一些经典结果.第二章中,主要是关于黎曼流形,子流形几何的基础知识介绍,并给出了各阶平均曲率的定义.第三章是本文的重要部分,首先对简单的情形进行讨论,即余维数为1的情形,从而得到了各阶平均曲率流短时间内的存在性及其演化方程.然后我们对任意余维数进行了研究,在给定一些条件下,也可以得出各阶平均曲率流短时间内的存在性. |
外文摘要: |
In this paper, some classical results of mean curvature flow are briefly described, and the existence and evolution equations of mean curvature flow solutions of every order in a compact without boundary Riemannian manifold under given conditions are studied. This paper is divided into three chapters. In the first chapter, the background of mean curvature flow is introduced. According to the classification of surface and codimension, some classical results of mean curvature flow are given. In the second chapter, the basic knowledge of Riemannian manifold and submanifold geometry is introduced, and the definition of mean curvature of each order is given. The third chapter is an important part of this paper. First of all, we discuss the simple case, i.e. the case of codimension one. Then we get the short-time existence and evolution equations of each order of mean curvature flow. Then we study any codimension case. Under some given conditions, we can also get the short-time existence of each order of mean curvature flow. |
参考文献总数: | 45 |
开放日期: | 2021-06-24 |