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Title Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
Creators Zhou Gang; Knopf Dan; Sigal Israel Michael
Organization American mathematical society
Imprint Providence, Rhode Island: AMS, 2018
Collection Электронные книги зарубежных издательств; Общая коллекция
Subjects Математика; Геометрия; mathematics; geometry
UDC 51; 514
Document type Other
File type Other
Language English
Rights Доступ по паролю из сети Интернет (чтение, печать)
Record key RU\SPSTU\edoc\60566
Record create date 2/13/2019

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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.

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