Isoperimetric Type Inequalities and Geometric Evolution Equations on Riemannian Manifolds


November 9, 2018 | 2:30 - 3:30 p.m.


Campbell Hall 443


Dr. Junfang Li


In this talk, we will survey some sharp isoperimetric type inequality and its generalization to quermassintegrals on hypersurfaces in Riemannian manifolds. Most of the talk will be about my joint work with Pengfei Guan (McGill University) over the past 10 years. We will focus on two main aspects of this research line: geometric inequalities as the goal and fully nonlinear PDE techniques as the tool. There have been a lot of active researches on related topics recently. One main idea of recent development is to extend these classical inequalities from Euclidean space to space forms, then to manifolds with warped product structures, and also to space like hypersurfaces in the black hole models from General Relativity. I will also list some of the open problems along this line.

Graduate and undergraduate students are welcome to attend. Most of the talk will be non-technical.