Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow

Häftad, Engelska, 2018

Av Gang Zhou, Dan Knopf, Israel Michael Sigal

1 169 kr

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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.

Produktinformation

Utgivningsdatum2018-05-01
Mått178 x 254 x undefined mm
Vikt175 g
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
FörlagAmerican Mathematical Society
ISBN9781470428402

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Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

IntroductionThe first bootstrap machineEstimates of first-order derivativesDecay estimates in the inner regionEstimates in the outer regionThe second bootstrap machineEvolution equations for the decompositionEstimates to control the parameters $a$ and $b$Estimates to control the fluctuation $\phi $Proof of the Main TheoremAppendix A. Mean curvature flow of normal graphsAppendix B. Interpolation estimatesAppendix C. A parabolic maximum principle for noncompact domainsAppendix D. Estimates of higher-order derivativesBibliography.