Mini-Course: Topics in Mean Curvature Flow and Singularities
Speaker:Ao Sun(Massachusetts Institute of Technology)
Location: 203， Mathematics Building
Date: 1月11日19:00-21:30、 1月12日19:00-21:00、1月13日15:00-17:00、1月15日19:00-21:00、1月16日19:00-21:00
Abstract: In the series of talks, I will discuss some fundamental results of mean curvature flow from the perspective of differential geometry.
The first part of the talks includes:
- Local estimate with techniques in parabolic PDEs,
- Huisken's monotonicity formula,
In particular, I will use curve shortening flow to illustrate the power of this techniques.
The second part of the talks includes the introduction to generalized mean curvature flow and some flows which are closely related to mean curvature flow, including:
- Brakke flow,
- Level set flow,
- Parabolic Allen-Cahn equation.
The third part of the talks concentrates on the analysis of the singularity. I will introduce self-shrinkers and discuss some properties of the self-shrinkers.
The fourth part of the talks concentrates on Colding and Minicozzi's seminal paper
Generic mean curvature flow I; generic singularities
I will introduce the main ideas of this paper. If time permits I will discuss how to generalize the idea to generic multiplicity one case.
