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Journal of Geometric Analysis

, Volume 19, Issue 1, pp 36–80 | Cite as

Neck Pinching Dynamics under Mean Curvature Flow

  • Zhou Gang
  • Israel Michael SigalEmail author
Article

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.

Keywords

Mean curvature flow Geometric flows Neckpinching Singularities formation Blowup Nonlinear PDEs 

Mathematics Subject Classification (2000)

35K55 35K57 53C44 

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Copyright information

© Mathematica Josephina, Inc. 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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