Abstract: In this talk, I will introduce a new notion of convexity in the unit sphere called horo-convexity, inspired by its analogue in hyperbolic space. For horo-convex hypersurfaces, we prove the smooth convergence of the Guan/Li inverse curvature flow and, as a consequence, establish the full set of quermassintegral inequalities on the sphere. If time permits, I will also discuss parallel results for the hypersurface with capillary boundary lying in the Euclidean unit ball. This talk is based on joint works with Julian Scheuer.

Brief biography: Shujing Pan is currently a postdoctoral researcher at Goethe-University Frankfurt. She obtained her Ph.D. at University of Science and Technology of China in 2021 under the supervision of Prof. Jiayu Li. Her research focuses on geometric flows and geometric inequalities.

Zoom: link          ID: 871 5029 4872             Password: 237909