报告题目:  Monotonicity along level set flow of p-capacitary functions and its applications

报告人: 夏超 教授 (厦门大学)

时间: 2024年8月2日 (周五) 10:00-11:00

地点: 理科楼A304

摘要:  In this talk, we present monotone quantities along the level set flow of $p$-capacitary functions in asymptotically flat $3$-manifolds with nonnegative scalar curvature. As applications, we prove geometric inequalities associated with $p$-capacitary functions, with rigidity on spatial Schwarzschild manifolds outside rotationally symmetric spheres, which generalizes Miao's result from $p=2$ to $1<p<3$. Moreover, we recover mass-to-$p$-capacity and $p$-capacity-to-area inequalities due to Bray-Miao and Xiao. Compare to $p=2$ case, there is no conformal relationship for general $p$-capacitary functions between Euclidean and Schwarzschild model. The monotonicity property follows from a direct analysis of a system of ODEs arising from $p$-capacitary functions in Schwarzschild model. This is joint work with Jiabin Yin and Xingjian Zhou.

邀请人: 李海中, 马辉, 陈大广