Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow
Zhou Gang · Dan Knopf · Israel Michael Siga
May 2018 · American Mathematical Soc.
Ebook
78
Pages
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About this ebook
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.
About the author
Zhou Gang: California Institute of Technology, Pasadena, California, USA,
Dan Knopf: University of Texas at Austin, Austin, Texas, USA,
Israel Michael Sigal: University of Toronto, Toronto, Ontario, Canada
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