Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
著者
書誌事項
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow
（Memoirs of the American Mathematical Society, no. 1210）
American Mathematical Society, c2018
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注記
Includes bibliographical references
May 2018, volume 253, number 1210 (fifth of 7 numbers)
内容説明・目次
内容説明
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.
目次
Introduction
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.
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