Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow

Dan Knopf author Israel Michael Sigal author Gang Zhou author

Format:Paperback

Publisher:American Mathematical Society

Published:30th Jun '18

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Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow cover

The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, the authors show that mcf solutions become singular in finite time by forming neckpinches, and they obtain detailed asymptotics of that singularity formation. The results show in a precise way that mcf solutions become asymptotically rotationally symmetric near a neckpinch singularity.

ISBN: 9781470428402

Dimensions: unknown

Weight: 175g

78 pages