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Convex sets evolving
by volume-preserving fractional mean curvature flows
Eleonora Cinti, Carlo Sinestrari and Enrico Valdinoci |
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Vol. 13 (2020), No. 7, 2149–2171
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Abstract |
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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. |
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Keywords
geometric evolution equations, fractional partial
differential equations, fractional perimeter, fractional
mean curvature flow, asymptotic behavior of solutions
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Mathematical Subject Classification 2010
Primary: 53C44, 35R11, 35B40
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Milestones
Received: 21 November 2018
Revised: 19 July 2019
Accepted: 6 September 2019
Published: 10 November 2020
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Authors |
| Eleonora Cinti | |
| Dipartimento di Matematica Università degli Studi di Bologna Bologna Italy |
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| Carlo Sinestrari | |
| Dipartimento di Ingegneria Civile e
Ingegneria Informatica Università di Roma “Tor Vergata” Rome Italy |
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| Enrico Valdinoci | |
| Department of Mathematics and
Statistics University of Western Australia Crawley, WA Australia |
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