偏微分方程系列报告-6月13-14日

题 目:Topics on harmonic maps and harmonic map heat flows

主讲人:Longzhi Lin (Rutgers University, USA)

邀请人:李岩岩 教授

地 点:后主楼1124

时 间:上午8:30-10:00,6月13日(周四)、14日(周五)

Abstract: The theory of harmonic maps and harmonic map heat flows has been a classic and intensely researched field of PDE and geometric analysis. In this series of talks we will start by introducing Tristan Riviere's conservation law for two dimensional conformally invariant variational problems and regularity for the weak solutions (with emphasis on weakly harmonic maps). We will then use these tools to show some recent results on the uniqueness of weakly harmonic maps and uniform convergence of harmonic map heat flow with small energy on a two dimensional disk.

题 目:Topics on Mean Curvature Flows in Space Forms

主讲人: Zheng Huang (The City University of New York, USA)

邀请人:李岩岩 教授

地 点:后主楼1124。

时 间:上午10:10-11:40,6月13日(周四)、14日(周五)

Abstract: Huisken in the 80s initiated a systematic study of the MCF(Mean Curvature Flow) equations. It is now a vast and extraordinarily active research field, with applications in differential geometry and mathematical physics. In this series, we start with several fundamental results of Huisken in Euclidean space, such as convexity estimates, contraction of strictly convex hypersurfaces, and his treatment of entire graphical setting with Ecker. We shall discuss Huisken's work on general Riemannian manifolds and then move to study the MCFs in other space forms, in particular, Huisken's work on spheres and Cabezas-Rivas-Miquel's work on hyperbolic space.

欢迎各位感兴趣的老师、研究生和本科生参加!

额外信息