报告人：翁良俊（意大利比萨高师）

题目: The capillary Gauss curvature flow and its applications

时间：1月6日（周二）上午11：00-12：00

地点：数学院新楼312

摘要: The classical Gauss curvature flow was introduced by Firey in 1974 as an idealized model for the abrasion of convex stones under random collisions on a beach. In 1985, Tso proved that convex hypersurfaces contract to a point in finite time under this flow. Later, in 1999, Andrews showed that in two dimensions the rescaled flow converges to a round sphere shape. Subsequent works by Andrews, Chow, Guan, Ni, and Brendle–Choi–Daskalopoulos established analogous convergence results in higher dimensions, as well as for the power Gauss curvature flow.

In this talk, based on joint work with Xinqun Mei and Guofang Wang, we discuss recent progress on capillary variants of the Gauss curvature flow and power Gauss curvature flow. In particular, we discuss the convergence properties of these flows, and their connections to the Lp-Minkowski problem.