題  目：Volume comparison with respect to scalar curvature

内容簡介：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.

報告人：中山大學  袁偉  副教授

報告人簡介：博士生導師，主要研究方向為幾何分析和廣義相對論，有十數篇論文發表在Trans. Amer. Math. Soc., Math. Ann., Calc. Var. PDE, J. Geom. Anal., Ann. Glob. Anal. Geom.等數學期刊上，目前，主持國家自然科學基金等科研項目。

時  間：2020年1月2日（周四）上午10：00始

地  點：南海樓三樓數學系師生研讨室

熱烈歡迎廣大師生參加!

太阳集团1088vip

2019年12月31日