Neck Pinching Dynamics Under Mean Curvature Flow

2007/08/21 by Zhou Gang, Israel Michael Sigal, Gang, Zhou +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0708.2938

38 Pages

arxiv created 2007/08/21 · openalex publication_date 2007/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution forms a "neck" which pinches in a finite time at a single point. We also obtain a detailed description of the neck pinching process.

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