Inverse mean curvature flow inside a cone in warped products

2017/05/13 by Li Chen, Chen, Li, Jing Mao +5
Mathematics · #35B45 #35K93 #53C42 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1705.04865

openalex publication_date 2017/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a convex cone in the prescribed warped product, we consider 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 along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.

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