时间：12月12日上午10:30

地点：3B205

讲座题目：Volume comparison with respect to scalar curvature

讲座摘要：

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.

个人简介：

袁伟现为中山大学数学学院教授，2015年毕业于University of California, San Cruz，获博士学位。从事微分几何的研究，已在Trans. Amer. Math. Soc., Math. Ann.,等杂志发表论文10余篇。