Time and place

Wednesday, 3.6.26, 14:15–15:45, SR 125/126 (E1)

Time and place

Tuesday, 2.6.26, 17:00–18:00, SR 404

Abstract

In this talk, we firstly introduce a capillary John ellipsoid theorem for capillary convex bodies in the Euclidean half-space \(\overline{\mathbb{R}^{n+1}_{+}}\). This theorem yields a non-collapsing estimate for capillary hypersurfaces, which provides a new approach to obtaining \(C^{0}\) estimates for solutions to some capillary curvature problems (including the capillary \(L_{p}\) Christoffel–Minkowski problem and the capillary \(L_{p}\) curvature problem). Then, as a further application, we study the capillary \(L_{p}\) dual Minkowski problem, establish existence for \(1<p\leq q\leq 3\), and improve existing results for the case \(p>q\) in \(\overline{\mathbb{R}^{3}_{+}}\).

Time and place

Tuesday, 2.6.26, 16:00–17:00, SR 404

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.

Time and place

Tuesday, 2.6.26, 14:15–15:15, Seminarraum 226, HH10

Abstract

TBA