Paper · Sep 26, 2022
A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
As on arXiv
Abstract
In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with -capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle . We prove that the solution of the flow remains to be strictly convex for , exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle . Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.
Comments: v2, 28 pages, 2 figures
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.
-
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
Topics Geometric inequalities, Free boundary & capillary, Volume-preserving & constrained flows · Shared terms “half space”, “Alexandrov Fenchel”, “Fenchel inequalities”
-
Inverse curvature flows for capillary hypersurfaces in the unit ball
Topics Geometric inequalities, Free boundary & capillary, Inverse mean curvature flow · Same author Bo Yang · Shared terms “capillary hypersurfaces”, “Alexandrov Fenchel”, “Fenchel inequalities”
-
Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
Topics Geometric inequalities, Free boundary & capillary, Inverse mean curvature flow · Shared terms “capillary hypersurfaces”, “Alexandrov Fenchel”, “Fenchel inequalities”
-
A constrained mean curvature flow and Alexandrov-Fenchel inequalities
Topics Geometric inequalities, Free boundary & capillary, Volume-preserving & constrained flows · Shared terms “Alexandrov Fenchel”, “Fenchel inequalities”, “half space”
-
A fully nonlinear locally constrained curvature flow for capillary hypersurface
Topics Geometric inequalities, Free boundary & capillary, Volume-preserving & constrained flows · Shared terms “capillary hypersurfaces”, “convex capillary”, “half space”
-
Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
Topics Geometric inequalities, Free boundary & capillary, Volume-preserving & constrained flows · Shared terms “Alexandrov Fenchel”, “Fenchel inequalities”, “locally constrained”
-
New quermassintegral and Poincaré type inequalities for non-convex domains
Topics Geometric inequalities, Inverse mean curvature flow, Volume-preserving & constrained flows · Same author Yingxiang Hu · Shared terms “Alexandrov Fenchel”, “locally constrained”, “positive time”
-
Alexandrov–Fenchel inequalities for convex domains in the sphere
Topics Geometric inequalities, Volume-preserving & constrained flows, Long-time existence & convergence · Same author Yong Wei · Shared terms “Fenchel inequalities”, “Alexandrov”, “strictly convex”
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.