Convexity and the Dirichlet problem of translating mean curvature flows

2016/12/12 by Li Ma, Ma, Li
Mathematics · Physics and Astronomy · #53C44 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.1612.03576

10 pages

arxiv created 2016/12/12 · openalex publication_date 2016/12/12 · arxiv updated 2016/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we propose a new evolving geometric flow (called translating mean curvature flow) for the translating solitons of hypersurfaces in Rⁿ⁺¹. We study the basic properties, such as positivity preserving property, of the translating mean curvature flow. The Dirichlet problem for the graphical translating mean curvature flow is studied and the global existence of the flow and the convergence property are also considered.

Related

• Some results on translating solitons of the mean curvature flow
• The translating soliton of mean curvature flow
• Convexity estimate for translating solitons of concave fully nonlinear extrinsic geometric flows in ℝⁿ⁺¹
• Maximum Principles and Consequences for γ-translators in ℝⁿ⁺¹ II
• On the topology of translating solitons of the mean curvature flow