Singularities of the area preserving curve shortening flow with a\n Neumann free boundary condition

2017/01/31 by Elena Mäder-Baumdicker, Mäder-Baumdicker, Elena · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Meromorphic and Entire Functions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1701.08948

openalex publication_date 2017/01/31 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28

Abstract

We consider the area preserving curve shortening flow with Neumann free\nboundary conditions outside of a convex domain or at a straight line. We give a\ncriterion on initial curves that guarantees the appearance of a singularity in\nfinite time. We prove that the singularity is of type II. Furthermore, if these\ninitial curves are convex, then an appropriate rescaling at the finite maximal\ntime of existence yields a grim reaper or half a grim reaper as limit flow. We\nconstruct examples of initial curves satisfying the mentioned criterion.\n

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• Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane
• Shrinkers of the area-preserving curve-shortening flow: Existence and saddle-point property

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