As on arXiv
Abstract
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 -capillary hypersurfaces and for those we introduce a new notion of convexity, which we call -horocap-convexity. For such hypersurfaces, we prove the convergence of a curvature flow of Guan/Li type with capillary boundary. Remarkably, we prove this result for a class of curvature functions which include all quotients of symmetric polynomials and, as a consequence, we obtain the full set of quermassintegral inequalities in the -horocap-convex case. In the strictly horocap-convex setting, we employ the flow to prove the geometric inequalities, while for the horocap-convex case and the characterization of the equality case, we develop new arguments which are interesting in their own right.
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Inverse curvature flows for capillary hypersurfaces in the unit ball
Topics Geometric inequalities, Free boundary & capillary, Other curvature flows · Same author Shujing Pan · Shared terms “unit ball”, “capillary hypersurfaces”, “Euclidean”
-
Quermassintegral inequalities for capillary hypersurfaces in a horoball
Topics Geometric inequalities, Free boundary & capillary, Other curvature flows · Shared terms “quermassintegral inequalities”, “capillary hypersurfaces”
-
Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
Topics Geometric inequalities, Free boundary & capillary, Other curvature flows · Shared terms “quermassintegral”, “Euclidean”
-
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
Topics Geometric inequalities, Free boundary & capillary, Other curvature flows · Shared terms “capillary hypersurfaces”, “quermassintegral”
-
Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
Topics Geometric inequalities, Free boundary & capillary, Other curvature flows · Shared terms “capillary hypersurfaces”, “quermassintegral”, “Guan”
-
A constrained mean curvature flow and Alexandrov-Fenchel inequalities
Topics Geometric inequalities, Free boundary & capillary · Shared terms “capillary quermassintegrals”
-
The quermassintegral preserving curvature flow for horo-convex hypersurfaces in the sphere
Topics Geometric inequalities, Other curvature flows · Same author Shujing Pan · Shared terms “quermassintegral”, “curvature functions”
-
Stability of quermassintegral inequalities along inverse curvature flows
Topics Geometric inequalities, Other curvature flows · Shared terms “quermassintegral inequalities”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.