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Research Report MRR98-009
Motion of hypersurfaces by Gauss curvature
Ben Andrews
Abstract:
We consider n-dimensional convex Euclidean hypersurfaces moving
with normal velocity proportional to a positive power 
of
the Gauss curvature. We prove that hypersurfaces contract to
points in finite time, and for ![$\alpha\in(1/(n+2),1/n]$](latex2html-dir/img2.gif)
we also
prove that in the limit the solutions evolve purely by homothetic
contraction to the final point. We prove existence and uniqueness
of solutions for non-smooth initial hypersurfaces, and develop
upper and lower bounds on the speed and the curvature independent
of initial conditions. Applications are given to the flow by
affine normal and to the existence of non-spherical homothetically
contracting solutions.
Select this link for a text-only version of this abstract.
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