MATH6022B - Topics in Geometry II - 2022/23

Announcement

• The guidelines for essay and presentation, together with some suggested topics, have be posted.
• The first class will take place on Jan 9, 2023.

General Information

Lecturer

• LI Man-chun Martin
  • Office: LSB 236
  • Tel: 3943-1851
  • Email:
  • Office Hours: By appointment

Time and Venue

• Lecture: Mon 2:30PM-5:15PM at LSB 222

Course Description

This is a graduate level topics course on geometry. This term we will focus on the geometric and analytic aspects of mean curvature flow. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. It also serves as a fundamental example that drives a lot of development in geometry and partial differential equations. In this course, we will give an overview of some foundational results like the evolution equations of geometric quantities and the convergence theorems of Gage- Hamilton and Huisken. We will also discuss about the analysis of singularities, both in the classical and weak setting, focusing mainly on the mean-convex case. We shall assume as prerequisite a working understanding of Riemannian Geometry (at the level of MATH5061), as well as basic knowledge on elliptic partial differential equations (at the level of MATH5022). In particular, prior exposure to other geometric flows (e.g. Ricci flow) is helpful but not absolutely required.

Pre-class Notes

• Course outline
• Presentations and essays

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.