Isoperimetric inequalities and scalar curvature rigidity

----微分几何讨论班（2025秋季）

程亮 教授

(华中师范大学)

报告时间：2025年10月17日（周五上午）10:00--11:00

腾讯会议ID：639-944-616

摘要：The rigidity part of Bishop-Gromov theorem implies that: If B(p,r) satisfies Rc≥(n-1)K on B(p,r), and if Vol(B(p,r))≥ Vol_K(B_K(p_K,r)), then B(p,r) is isometric to B_K(p_K,r), where B_K(p_K,r) denotes the r-ball in space forms. Our recent results extend the rigidity part of Bishop-Gromov's theorem to the scalar curvature case in the following sense: when the Ricci curvature condition is replaced with a lower bound n(n-1)K on the scalar curvature, and assume that the volume requirement is strengthened by requiring that the isoperimetric profile is no less than that of the space form, the rigidity conclusion remains valid.

报告人简介：华中师范大学副教授，博士生导师。一直从事几何分析及曲率流研究，在此的方向上已经发表SCI论文十余篇，研究工作分别发表在《Trans.Amer.Math.Soc》、《Adv. Math.》、《Math. Ann.》、《Commun.Anal.Geom.》、《J. Differ. Equations.》、《J.Geom.Anal.》等SCI杂志上，现主持国家自然科学基金面上项目一项。

邀请人：胡鹰翔                  

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