Mean Curvature Flows of Closed Hypersurfaces in Warped Product Manifolds

2017/08/21 by Zheng Huang, Zhou Zhang, Huang, Zheng +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1708.06049

openalex publication_date 2017/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the mean curvature flows in a class of warped product manifolds with closed hypersurfaces fibering over ℝ. In particular, we prove that under natural conditions on the warping function and Ricci curvature bound for the ambient space, there exists a large class of closed initial hypersurfaces, as geodesic graphs over the totally geodesic hypersurface Σ, such that the mean curvature flow starting from S₀ exists for all time and converges to Σ.

Related

• Mean curvature flows of graphs sliding off to infinity in warped product manifolds
• Mean curvature flow in Fuchsian manifolds
• Mean Curvature Type Flows of Graphs in Product Manifolds
• Mean curvature flow of graphs in warped products
• On the inverse mean curvature flow in warped product manifolds