New stability results for spheres and Wulff shapes

New stability results for spheres and Wulff shapes

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving...

Full description

Bibliographic Details
Main Author: Roth Julien
Format: Article
Language:English
Published: Sciendo 2018-12-01
Series:Communications in Mathematics
Subjects:
hypersurfaces
anisotropic mean curvatures
wulff shape
almost umibilcal
53c42
53a10
Online Access:https://doi.org/10.2478/cm-2018-0012
id doaj-a469da47daf846c593895d6aff36fe0b
record_format Article
spelling doaj-a469da47daf846c593895d6aff36fe0b2021-09-06T19:22:06ZengSciendoCommunications in Mathematics2336-12982018-12-0126215316710.2478/cm-2018-0012cm-2018-0012New stability results for spheres and Wulff shapesRoth Julien0Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, 5, boulevard Descartes, Cité Descartes, 77454Marne-la-Vallée cedex 2, FranceWe prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].https://doi.org/10.2478/cm-2018-0012hypersurfacesanisotropic mean curvatureswulff shapealmost umibilcal53c4253a10
collection DOAJ
language English
format Article
sources DOAJ
author Roth Julien
spellingShingle Roth Julien
New stability results for spheres and Wulff shapes
Communications in Mathematics
hypersurfaces
anisotropic mean curvatures
wulff shape
almost umibilcal
53c42
53a10
author_facet Roth Julien
author_sort Roth Julien
title New stability results for spheres and Wulff shapes
title_short New stability results for spheres and Wulff shapes
title_full New stability results for spheres and Wulff shapes
title_fullStr New stability results for spheres and Wulff shapes
title_full_unstemmed New stability results for spheres and Wulff shapes
title_sort new stability results for spheres and wulff shapes
publisher Sciendo
series Communications in Mathematics
issn 2336-1298
publishDate 2018-12-01
description We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp-sense is W2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].
topic hypersurfaces
anisotropic mean curvatures
wulff shape
almost umibilcal
53c42
53a10
url https://doi.org/10.2478/cm-2018-0012
work_keys_str_mv AT rothjulien newstabilityresultsforspheresandwulffshapes
_version_ 1717772706847391744

Similar Items