中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：夏超 教授（厦门大学）
题 目： Two geometric inequalities for hypersurfaces with boundary in convex domains
时 间：2024.08.06（星期二）15：00-16：00
地 点：思源楼S713
摘 要：In this talk, we show two kinds of sharp geometric inequalities, one is Heintze-Karcher-type inequality and the other is Willmore-type inequality, for hypersurfaces with boundary in convex domains. The arguments for the proof share similarity on using parallel hypersurfaces in the spirit of Heintze-Karcher, but in two opposite directions. We also give the generalization to the anisotropic case and to the case of manifolds with nonnegative Ricci curvature.The talk is based on joint works with Xiaohan Jia, Guofang Wang and Xuwen Zhang.
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报告人：Professor Jiakun Li (University of Wollongong)
题 目：Some applications of optimal transportation
时 间：2024.08.06（星期二）16：00-17：00
地 点：思源楼S713
摘 要：In this talk, we will introduce some interesting applications of optimal transportation in various fields including a reconstruction problem in cosmology; a brief proof of isoperimetric and Brunn-Minkowski inequalities in geometry; and an application in image recognition relating to a transport between hypercubes. This talk is based on a series of joint work with Shibing Chen, Xu-Jia Wang, and with Gregoire Loeper.
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