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.
CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS / CINTI E.; SINESTRARI C.; VALDINOCI E.. - In: ANALYSIS & PDE. - ISSN 2157-5045. - STAMPA. - 13:7(2020), pp. 2149-2171. [10.2140/apde.2020.13.2149]
CONVEX SETS EVOLVING BY VOLUME-PRESERVING FRACTIONAL MEAN CURVATURE FLOWS
CINTI E.;SINESTRARI C.;VALDINOCI E.
2020
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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