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Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow /
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, an...
| Call Number: | Libro Electrónico |
|---|---|
| Main Authors: | , , |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
[2018]
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1210. |
| Subjects: | |
| Online Access: | Texto completo |
Table of 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.
- 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.
- Appendix C.A parabolic maximum principle for noncompact domainsAppendix D. Estimates of higher-order derivatives; Bibliography; Back Cover.