Abstract:
In this work we study the behaviour of compact, smooth, immersed manifolds with boundary, which move under the mean curvature flow in Euclidean space. We thereby prescribe the Neumann boundary condition in a purely geometric manner by requiring a vertical contact angle between the unit normal fields of the immersions and a given, smooth hypersurface S. We prove a very general existence result and study the formation of the singularity which occurs if S is a convex, umbilic hypersurface and the initial hypersurface is strictly convex.
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