4 papers
The quermassintegral preserving curvature flow for horo-convex hypersurfaces in the sphere
Sara Albert-Niclòs, Esther Cabezas-Rivas, Shujing Pan
We introduce fully nonlinear curvature flows of horo-convex hypersurfaces in the sphere that preserve an arbitrarily prescribed spherical quermassintegral. The non-local normalizat…
Capillary quermassintegral inequalities in the unit ball
Shujing Pan, Julian Scheuer
This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle . Such hypersurfaces are called $…
The quermassintegral inequalities for horo-convex domains in the sphere
Shujing Pan, Julian Scheuer
We study a new notion of convexity for subsets of the unit sphere, which closely resembles the horo-convexity for subsets of the hyperbolic space. We call this notion, accordingly,…
Inverse curvature flows for capillary hypersurfaces in the unit ball
Shujing Pan, Bo Yang
In this paper, we study inverse curvature flows for strictly convex, capillary hypersurfaces in the unit Euclidean ball. We establish the existence and convergence results for a cl…