Publication Details

Wheeler, V. (2014). Non-parametric radially symmetric mean curvature flow with a free boundary. Mathematische Zeitschrift, 276 (1-2), 281-298.


We study the mean curvature flow of radially symmetric graphs with prescribed contact angle on a fixed, smooth hypersurface in Euclidean space. In this paper we treat two distinct problems. The first problem has a free Neumann boundary only, while the second has two disjoint boundaries, a free Neumann boundary and a fixed Dirichlet height. We separate the two problems and prove that under certain initial conditions we have either long time existence followed by convergence to a minimal surface, or finite maximal time of existence at the end of which the graphs develop a curvature singularity. We also give a rate of convergence for the singularity. 2013 Springer-Verlag Berlin Heidelberg.



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