报告题目: Volume comparison with respect to scalar curvature
报告人：袁伟 副教授
报告人单位： 中山大学
报告时间：2019年5月24日，上午10：00-11:00
报告地点：四牌楼校区逸夫建筑馆1511
报告摘要:
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 global results, we give volume comparison for metrics near stable Einstein metrics. As applications, we give a partial affirmative answer to Schoen’s conjecture about hyperbolic manifolds, which recovers a result due to Besson-Courtois-Gallot with a different approach. We also provide a partial affirmative answer to a conjecture proposed by Bray concerning the positive scalar curvature case.
报告人介绍：
袁伟博士，中山大学副教授。2008年本科毕业于南开大学，2010年于中国科学技术大学取得理学硕士学位后赴加州大学圣克鲁斯分校（UC Santa Cruz）学习并于2015年取得理学博士学位。主要研究方向为几何分析和广义相对论。目前已在Math. Ann., Trans. AMS, Calculus of Variations and PDE等学术期刊上发表研究论文8篇。