题目：New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms

报告人：吴洁教授，浙江大学

报告地点：东区第五教学楼5202

报告时间：7月2日，14：00

摘要：In this talk, we discuss some new weighted geometric inequalities for hypersurfaces in space forms. First, we obtain a new kind of weighted Alexandrov-Fenchel type inequalities for star-shaped and 𝑘-convex hypersurface in Euclidean space. As an application, we obtain a lower bound for the outer radius in terms of the curvature integrals. Second, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski inequalities for static convex hypersurfaces in hyperbolic space and for convex hypersurfaces in the sphere.