报告题目： Deformations of the Scalar Curvature and the Mean Curvature

报告人： 盛弘毅 博士

报告时间： 2023-09-14   15:00-15：50

报告地点： 腾讯会议 498 753 632

报告摘要： On a compact manifold with boundary, the map consisting of the scalar

curvature in the interior and the mean curvature on the boundary is a local surjection at

generic metrics. We prove that this result may be localized to compact subdomains in an

arbitrary Riemannian manifold with boundary, as motivated by an attempt to generalize the

Riemannian Penrose inequality in dimension 8. This result is a generalization of Corvino's

result about localized scalar curvature deformations; however, the existence part needs to be

handled delicately since the problem is non-variational. For nongeneric cases, we give a

classification theorem for domains in space forms and Schwarzschild manifolds, and show

the connection with positive mass theorems.

报告人简介： 本科毕业于浙江大学，美国加州大学尔湾分校基础数学博士， 加利福尼亚大学圣迭戈分校博士后，师从著名几何学家Richard Schoen，主要从事几何拓扑学，偏微分方程相关研究。