几何分析研讨班

 

 

报告人:孙俊 副教授 (武汉大学)

题  目:Volume Comparison Theorem With Respect to Scalar Curvature

时  间:2021.01.18(星期一), 09:00-11:00
      2021.01.20(星期三), 09:00-11:00
      2021.01.22(星期五), 09:00-11:00

地  点:腾讯会议ID  348 6898 7444

摘  要:Abstract: The classical volume comparison theorem says that if the Ricci curvature of a Riemannian manifold M is greater than or equal to (n-1), then its volume is less than or equal to that of the unit round sphere, with equality holds if and only if M is isometric to the round sphere. In this series of lectures, we will talk about volume comparison theorem with respect to scalar curvature. It consists of three parts:

Part I: We will talk about Bray’s thesis (Stanford University, 1997), which conjectured that if the scalar curvature of M is greater than or equal to n(n-1), and the Ricci curvature of M is bounded from below by \epsilon, then the volume of M is less than or equal to that of the unit round sphere. Bray proved this conjecture when the dimension of M is 3.

Part II: We will first recall Gursky-Vialovsky’s result, which provided an explicit lower bound 1/2 for \epsilon when the dimension of M is 3. Then we will talk about Brendle’s result, which shows the rigidity for \epsilon=1/2 when the dimension of M is 3.

Part III: We will talk about some recent progress on the volume comparison theorem with respect to scalar curvature in high dimensions.

附件
相关文档