时间：2026年10月21日（周三）16:00-17:00
地点: E14-301
报告人：中国科学技术大学，韦勇
报告题目：Alexandrov-Fenchel inequalities for convex domains in the sphere
报告摘要：We prove the full family of Alexandrov-Fenchel inequalities for spherical quermassintegrals of smooth weakly convex domains contained in an open hemisphere, with equality if and only if the domain is a geodesic ball. For strictly convex hypersurfaces, we introduce a globally constrained curvature flow which preserves one quermassintegral and decreases the next one. We establish uniform curvature estimates by combining a pinching estimate, a support function argument, and spherical polarity. As a consequence, the flow exists for all time and converges smoothly and exponentially to a geodesic sphere. The monotonicity of the quermassintegrals gives the full family of Alexandrov-Fenchel inequalities. A short-time mean curvature flow approximation and a localized rigidity argument extend the result to weakly convex domains. This is joint work with my students Tianci Luo and Rong Zhou.
