Neck Pinching Dynamics under Mean Curvature Flow
نویسندگان
چکیده
منابع مشابه
Neck Pinching Dynamics Under Mean Curvature Flow
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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We study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are C3-close to round, but without assuming rotational symmetry or positive mean curvature, we show that mcf solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that mcf solutions...
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2008
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-008-9050-y