We consider a convex Euclidean hypersurface that evolves by a volume- or area-preserving flow with speed given by a general nonhomogeneous function of the mean curvature. For a broad class of possible speed functions, we show that any closed convex hypersurface converges to a round sphere. The proof is based on the monotonicity of the isoperimetric ratio, which allows to control the inner radius and outer radius of the hypersurface and to deduce uniform bounds on the curvature by maximum principle arguments.

Bertini, M.C., & Sinestrari, C. (2018). Volume-preserving nonhomogeneous mean curvature flow of convex hypersurfaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 197(4), 1295-1309 [10.1007/s10231-018-0725-0].

Volume-preserving nonhomogeneous mean curvature flow of convex hypersurfaces

Sinestrari, Carlo
2018

Abstract

We consider a convex Euclidean hypersurface that evolves by a volume- or area-preserving flow with speed given by a general nonhomogeneous function of the mean curvature. For a broad class of possible speed functions, we show that any closed convex hypersurface converges to a round sphere. The proof is based on the monotonicity of the isoperimetric ratio, which allows to control the inner radius and outer radius of the hypersurface and to deduce uniform bounds on the curvature by maximum principle arguments.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
Settore MAT/03 - Geometria
English
Con Impact Factor ISI
Asymptotic behaviour; Geometric flows; Isoperimetric ratio
Carlo Sinestrari was partially supported by the research group GNAMPA of INdAM (Istituto Nazionale di Alta Matematica)
http://springerlink.metapress.com/app/home/journal.asp?wasp=cmw755wvtg0qvm8kjj1q&referrer=parent&backto=linkingpublicationresults,1:108198,1
Bertini, M.C., & Sinestrari, C. (2018). Volume-preserving nonhomogeneous mean curvature flow of convex hypersurfaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 197(4), 1295-1309 [10.1007/s10231-018-0725-0].
Bertini, Mc; Sinestrari, C
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/197922
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