A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone

2021/04/18 by Jing Mao, Qiang Tu, Mao, Jing +1 · 1 citation
Mathematics · #35K10 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.08884

openalex publication_date 2021/04/18 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

Given a smooth convex cone in the Euclidean (n+1)-space (n≥2), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve by a class of inverse curvature flows, then, by using the convexity of the cone in the derivation of the gradient and Hölder estimates, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of a round sphere as time tends to infinity.

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• An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ℝⁿ⁺¹₁

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