Translating graphs by mean curvature flow

2012/12/27 by Leili Shahriyari, Shahriyari, Leili · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG

paper · pdf · doi:10.48550/arxiv.1212.6418

openalex publication_date 2012/12/27 · arxiv created 2014/06/04 · arxiv updated 2014/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this work is studying translating graphs by mean curvature flow in \Real³. We prove non-existence of complete translating graphs over bounded domains in \Real². Furthermore, we show that there are only three types of complete translating graphs in \Real³; entire graphs, graphs between two vertical planes, and graphs in one side of a plane. In the last two types, graphs are asymptotic to planes next to their boundaries. We also prove stability of translating graphs and then we obtain a pointwise curvature bound for translating graphs in \Real³.

Citations

• Curvature estimates for minimal hypersurfaces

Cited by

• A monotonicity formula and Type-II singularities for the mean curvature flow
• Stability of vertical and radial graphs in the Euclidean space with density

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