On the regularity of the Ricci flow
Date Issued
2012
Date
2012
Author(s)
Chen, Chih-Wei
Abstract
This thesis consists of four chapters and an appendix.
The first chapter is dedicated to the fundamental ideas of the theory of Ricci flow, which shows how our works are connected to the whole story. In the second chapter, we construct a solution of Ricci flow on a rotationally symmetric manifold such that it remains a complete manifold at the maximal time. We also derive a noncollapsing property for certain ancient solutions near their maximal times. Both of these two results are related to the regularity of limits of solutions. In the third chapter, we show that a first order Shi-type estimate holds for Ricci tensor on manifolds which satisfy the weak Bianchi inequality. The last chapter is concerned with expanding gradient Ricci solitons. There we discuss the classification problem and show that every tangent cone at infinity of an expanding soliton with fast-than-quadratic-decay curvature must be $mathbb{R}^n$.
Subjects
Ricci flow
Ricci soliton
Type
thesis
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