Mean Curvature Flow of Cones

Mean Curvature Flow of Cones

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Sigurd Angenent, University of Wisconsin, Madison
Fine Hall 214

For smooth initial hypersurfaces one has short time existence and uniqueness of solutions to Mean Curvature Flow.  For general initial data Brakke showed that varifold solutions exist, but that they need not be unique if the initial data are non smooth.  In this talk I will discuss the multitude of solutions to MCF that exist if the initial hypersurface is a cone that is smooth except at the origin.  Some of the examples go back to older work with Chopp, Ilmanen, and Velazquez, other examples are recent.