题  目：Volume comparison with respect to scalar curvature

内容简介：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.

报告人：中山大学  袁伟  副教授

报告人简介：博士生导师，主要研究方向为几何分析和广义相对论，有十数篇论文发表在Trans. Amer. Math. Soc., Math. Ann., Calc. Var. PDE, J. Geom. Anal., Ann. Glob. Anal. Geom.等数学期刊上，目前，主持国家自然科学基金等科研项目。

时  间：2020年1月2日（周四）上午10：00始

地  点：南海楼三楼数学系师生研讨室

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信息科学技术学院

2019年12月31日