Title

Mean curvature flow with free boundary in embedded cylinders or cones and uniqueness results for minimal hypersurfaces

RIS ID

113321

Publication Details

Wheeler, V. (2017). Mean curvature flow with free boundary in embedded cylinders or cones and uniqueness results for minimal hypersurfaces. Geometriae Dedicata, 190 (1), 157-183.

Abstract

In this paper we study the mean curvature flow of embedded disks with free boundary on an embedded cylinder or generalised cone of revolution, called the support hypersurface. We determine regions of the interior of the support hypersurface such that initial data is driven to a curvature singularity in finite time or exists for all time and converges to a minimal disk. We further classify the type of the singularity. We additionally present applications of these results to the uniqueness problem for minimal hypersurfaces with free boundary on such support hypersurfaces; the results obtained this way do not require a-priori any symmetry or topological restrictions.

Grant Number

ARC/DP150100375

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