Evolution of hypersurfaces in central force fields

Oliver Schnürer and Knut Smoczyk

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Submission date: 15. Jan. 2001
Pages: 25
published in: Journal für die reine und angewandte Mathematik, 550 (2002), p. 77-95 
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Abstract:
We consider flows of hypersurfaces in Rⁿ⁺¹ decreasing the energy induced by radially symmetric potentials. These flows are similar to the mean curvature flow but different phenomena occur. We show for a natural class of potentials that hypersurfaces converge smoothly to a uniquely determined sphere if they satisfy a strengthened starshapedness condition at the beginning.