Gauss curvature flow


题目:Gauss curvature flow

报告人:Dr.  Kyeongsu Choi  (Columbia University & MIT, USA)

时间:201773(周一), 75(周三), 77(周五), 710(周一), 712(周三)  上午9:00-11:00

地点: 理科楼A404

摘要:The Gauss curvature flow is an evolution of a convex hypersurface by its Gauss curvature which describes the shape of worn stones.

It has been widely studied not only in Geometry but also in Analysis, because it is a natural parabolic Monge-Amp\`ere equation. We will study its inverse concavity, divergence structure, and non-degenerate ellipticity to obtain monotonicity formulas and interior regularity.

We will also investigate free boundary problems and their application to the classification of the closed self-similar solutions.


1. Caffarelli-Nirenberg-Spruck trick and standard Pogorelov computations (for new students)

2. Techniques in Pogorelov computations

3. Free boundary problems

4. Classification of self-shrinkers  

5. Monotonicity



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