Speaker
Pengfei Guan
Abstract
We discuss flow approach for isoperimetric problems. Given two geometric functionals, one would like to find optimal relationship between them (e.g., classical isoperimetric inequality for volume and surface area). This can be stated as a variational problem: find extremal of one functional with the other constrained. One would like to design flows serving as good paths to the optimal solution. This consideration leads to a new class of interesting curvature flows, mean curvature type and inverse mean curvature type. The longtime existence and convergence are the main focus. We discuss some new results and open problems.