Extension of two-dimensional mean curvature flow with free boundary

2018/07/09 by Siao-Hao Guo, Guo, Siao-Hao · 1 citation
Mathematics · #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.1807.02922

openalex publication_date 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a mean curvature flow of compact, embedded C² surfaces satisfying Neumann free boundary condition on a mean convex, smooth support surface in 3-dimensional Euclidean space, we show that it can be extended as long as its mean curvature and perimeter stay uniformly bounded along the flow.

Citations

• Fully nonlinear parabolic equations in two space variables

Cited by

• Contracting convex surfaces by mean curvature flow with free boundary on convex barriers

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