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Geometric Analysis and Partial Differential Equations Seminar
April 17, 2013 @ 10:30 am - 11:30 pm
Dr. James McCoy (University of Wollongong)
Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions
Inspired by earlier results on the mean curvature flow, and recent investigations of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we consider contraction of axially symmetric hypersurfaces by convex, degree-one homogeneous fully nonlinear functions of curvature. With a natural class of Neumann boundary conditions, we show that evolving hypersurfaces exist for a finite maximal time. The maximal time is characterised by a curvature singularity at either boundary. Some results continue to hold in the cases of mixed Neumann-Dirichlet boundary conditions and more general curvature-dependent speeds. This is joint work with Fatemah Mofarreh and Graham Williams.