On The Free Boundary Mean Curvature Flow

Download or read book On the Free-boundary Mean Curvature Flow written by Nicholas Edelen and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the free-boundary mean curvature flow. This is an evolution of surfaces by ``steepest descent for area, '' while preserving the Neumann-type condition that all the surfaces meet some fixed barrier orthogonally. For example, a bubble in a sink. We first prove the Huisken-Sinestrari convexity estimates for free-boundary mean curvature flow, which classifies ``type-II'' singularities. We then develop the notion of weak free-boundary mean curvature flow, extending Brakke's original definition, and proving a local regularity theorem. We also prove a geometric eigenvalue gap estimate, extending results of Ashbaugh-Benguria and Benguria-Linde.