We consider the volume-preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long-time asymptotics approach round spheres. The proofs are based on a priori estimates on the inner and outer radii of the solutions.
Cinti, E., Sinestrari, C., Valdinoci, E. (2020). CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS. ANALYSIS & PDE, 13(7), 2149-2171 [10.2140/apde.2020.13.2149].
CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS
SINESTRARI C.;VALDINOCI E.
2020-01-01
Abstract
We consider the volume-preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long-time asymptotics approach round spheres. The proofs are based on a priori estimates on the inner and outer radii of the solutions.File in questo prodotto:
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