Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow

Download or read book Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow written by Zhou Gang and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.