Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow

Gang Zhou, California Institute of Technology, Pasadena, California.Dan Knopf, University of Texas at Austin, Texas.Israel Michael Sigal, University of Toronto, Ontario, Canada.

• IntroductionThe first bootstrap machineEstimates of first-order derivativesDecay estimates in the inner regionEstimates in the outer regionThe second bootstrap machineEvolution equations for the decompositionEstimates to control the parameters $a$ and $b$Estimates to control the fluctuation $\phi $Proof of the Main TheoremAppendix A. Mean curvature flow of normal graphsAppendix B. Interpolation estimatesAppendix C. A parabolic maximum principle for noncompact domainsAppendix D. Estimates of higher-order derivativesBibliography.