Scalar Curvature Compactness for Warped Product Circles over Spheres with Varying Base Metrics

报告人：王常亮（同济大学）

时  间：2026年6月9日11:00

地  点：海韵园实验楼S204

内容摘要:

Scalar curvature lower bounds impose strong global restrictions on smooth Riemannian manifolds, but their compactness theory is much less understood than the corresponding theories for sectional or Ricci curvature. Gromov and Sormani conjectured that a sequence of three-dimensional Riemannian manifolds with nonnegative scalar curvature and suitable uniform geometric bounds should have a subsequence which converges in the intrinsic flat sense to a limit space with some generalized notion of nonnegative scalar curvature. In this talk, I will discuss this conjecture and present recent progress in several model settings. In particular, I will report on recent joint work with Zhixin Wang, in which we establish scalar curvature compactness results for warped product circles over spheres with varying base metrics.

个人简介：

王常亮，同济大学特聘研究员。2008年、2011年分别于中国科学技术大学获学士、硕士学位，2016年于加州大学圣塔芭芭拉分校获博士学位，师从戴先哲教授。曾在加拿大麦克马斯特大学和德国马克斯·普朗克数学研究所从事博士后研究，2020年起任职于同济大学。研究方向是微分几何与几何分析，主要研究非负数量曲率流形类的正则性与紧性、Einstein度量稳定性等问题，相关工作发表于Math. Ann., Trans. Amer. Math. Soc., Calc. Var. PDE., Comm. Anal. Geom., Sci. China Math.等期刊。

联系人：桂耀挺