Minimal Submanifolds and Mean Curvature Flow
Date Issued
2004
Date
2004
Author(s)
Lee, Kuo-Wei
DOI
en-US
Abstract
The study of minimal submanifolds has a long and rich history. When the minimal submanifold is of non-parametric form, many beautiful results have been proved in the case of codimension one. However, the situation in higher codimension is quite different and is much less studied.
The first part of this thesis summarizes and gives a comparison between the results in codimension one and higher codimension. Chapter 1, I introduce basic definitions and terminology as preliminaries. Results on the Dirichlet problem of minimal surface systems are discussed in chapter 2. In section 2.1, I summerize the results, and explain in more detail in section 2.2 and 2.3 about some counterexample in higher codimension. Another important aspect of minimal submanifolds, namely Bernstein
theorem, is studies in chapter 3. In the second part of this thesis, I study some resent papers of M. T. Wang.
With the aid of an additional form, he makes a big progress in mean curvature flow in higher codimension and proves many interesting results. The main theme of my study in master program is to understand his results and method.
In chapter 4, I introduce the the main idea of Wang's work to fill in some missing arguments in his paper.
Subjects
極小子流形
均曲率流
mean curvature flow
minimal submanifolds
Type
thesis
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