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OverviewThe 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. Full Product DetailsAuthor: Gang Zhou , Dan Knopf , Israel Michael SigalPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.175kg ISBN: 9781470428402ISBN 10: 1470428407 Pages: 78 Publication Date: 30 June 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction The first bootstrap machine Estimates of first-order derivatives Decay estimates in the inner region Estimates in the outer region The second bootstrap machine Evolution equations for the decomposition Estimates to control the parameters $a$ and $b$ Estimates to control the fluctuation $\phi $ Proof of the Main Theorem Appendix A. Mean curvature flow of normal graphs Appendix B. Interpolation estimates Appendix C. A parabolic maximum principle for noncompact domains Appendix D. Estimates of higher-order derivatives Bibliography.ReviewsAuthor InformationGang Zhou, California Institute of Technology, Pasadena, California. Dan Knopf, University of Texas at Austin, Texas. Israel Michael Sigal, University of Toronto, Ontario, Canada. Tab Content 6Author Website:Countries AvailableAll regions |
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