题目：Volume comparison with respect to scalar curvature

报告人：袁伟 副教授（中山大学）

摘要：In Riemannian geometry, volume comparison theorem is one of the most fundamental results. The classic results concern volume comparison involving restrictions on Ricci curvature. In this talk, we will investigate the volume comparison with respect to scalar curvature. In particular, we show that one can only expect such results for small geodesic balls of metrics near V-static metrics. As for closed manifolds, we give a volume comparison theorem for metrics near stable Einstein metrics. In particular, it provides partially affirmative answers to both a conjecture of Schoen about hyperbolic manifolds and a conjecture proposed by Bray concerning the positive scalar curvature case respectively. 

时间：2021年8月6日周五上午9:00-11:00

腾讯会议：872 169 809