报告题目：Sobolev to Perelman: a trip to W-functionals
时间：2021-03-23 (星期二) 15:30 ~ 2021-03-23 (星期二) 17:00
地点：腾讯会议（ID：570 741 001）
主讲：北京科技大学马力教授
主办：数学与信息学院, 福建省分析数学及应用重点实验室
参加对象：数学系老师和研究生
报告摘要：In this talk, we start from discussing the Sobolev inequality and its variants. Then we consider the extremals of Perelman's W-functional, which is a log Sobolev in the Euclidean space. We mainly study properties of the lambda constants and the existence of ground states of Perelman's famous W-functional from a variational formulation. We show the estimation of lambda constant of G.Perelman and the existence of ground states of his W-functional both on a complete non-compact Riemannian manifold (M,g). We also introduce a new invariant constant d(M,g). For the existence of the ground states we use Lions' concentration-compactness method.
报告人简介：马力，北京科技大学教授、博导，主要从事几何分析与偏微分方程的研究，已在Adv. Math, ARMA, JMPA, CV &PDE, J. Funct. Anal., Comm. Math.Phy., JDE等多个数学领域的著名期刊上发表论文。