Neck Pinching Dynamics Under Mean Curvature Flow

Mathematics – Analysis of PDEs

Scientific paper

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38 Pages

Scientific paper

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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