Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow / Gang Zhou, Dan Knopf, Israel Michael Sigal.

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Zhou, Gang (Mathematics professor) (Author), Knopf, Dan, 1959- (Author), Sigal, Israel Michael, 1945- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2018]
Series:Memoirs of the American Mathematical Society ; no. 1210.
Subjects:
Evolution equations > Asymptotic theory.
Asymptotic expansions.
Curvature.
Singularities (Mathematics)
MATHEMATICS > Geometry > General.
Singularidades (Matemáticas)
Ecuaciones de evolución
Desarrollos asintóticos
Asymptotic expansions
Curvature
Evolution equations > Asymptotic theory
Online Access:Click for online access
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.

Similar Items