| Description |
1 online resource (v, 78 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 253, number 1210 |
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Memoirs of the American Mathematical Society ; no. 1210. 0065-9266
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| Contents |
Cover; Title page; Chapter 1. Introduction; 1.1. What we study; 1.2. Basic evolution equations; 1.3. Implied evolution equations; Chapter 2. The first bootstrap machine; 2.1. Input; 2.2. Output; 2.3. Structure; Chapter 3. Estimates of first-order derivatives; Chapter 4. Decay estimates in the inner region; 4.1. Differential inequalities; 4.2. Lyapunov functionals of second and third order; 4.3. Lyapunov functionals of fourth and fifth order; 4.4. Estimates of second- and third-order derivatives; Chapter 5. Estimates in the outer region; 5.1. Second-order decay estimates |
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5.2. Third-order decay estimates5.3. Third-order smallness estimates; Chapter 6. The second bootstrap machine; 6.1. Input; 6.2. Output; 6.3. Structure; Chapter 7. Evolution equations for the decomposition; Chapter 8. Estimates to control the parameters and; Chapter 9. Estimates to control the fluctuation; 9.1. Proof of estimate (7.12); 9.2. Proof of estimate (7.13); 9.3. Proof of estimate (7.15); 9.4. Proof of estimate (7.14); Chapter 10. Proof of the Main Theorem; Appendix A. Mean curvature flow of normal graphs; Appendix B. Interpolation estimates |
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Appendix C.A parabolic maximum principle for noncompact domainsAppendix D. Estimates of higher-order derivatives; Bibliography; Back Cover |
| Summary |
The authors study noncompact surfaces evolving by mean curvature flow (mcf). For an open set of initial data that are Ĉ3-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 |
| Notes |
"May 2018, volume 253, number 1210 (fifth of 7 numbers)." |
| Bibliography |
Includes bibliographical references (page 78) |
| Notes |
Print version record |
| Subject |
Evolution equations -- Asymptotic theory.
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Asymptotic expansions.
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Curvature.
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Singularities (Mathematics)
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MATHEMATICS -- Geometry -- General.
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Singularidades (Matemáticas)
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Ecuaciones de evolución
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Desarrollos asintóticos
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Asymptotic expansions
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Curvature
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Evolution equations -- Asymptotic theory
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Singularities (Mathematics)
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| Form |
Electronic book
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| Author |
Knopf, Dan, 1959- author.
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Sigal, Israel Michael, 1945- author.
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American Mathematical Society, publisher.
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| ISBN |
9781470444150 |
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1470444151 |
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