Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow (Memoirs of the American Mathematical Society)

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