Pinching of the First Eigenvalue of the Laplacian and almost-Einstein Hypersurfaces of the Euclidean Space

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dc.creatorRoth, Julien
dc.date2007-02-07
dc.date.accessioned2026-07-07T09:28:56Z
dc.date.available2026-07-07T09:28:56Z
dc.descriptionIn this paper, we prove new pinching theorems for the first eigenvalue of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for the first eigenvalue in terms of higher order mean curvatures. We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost isometric to a standard sphere. Moreover, as a corollary, we show that a hypersurface of the Euclidean space which is almost Einstein is diffeomorpic and almost isometric to a standard sphere.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0702174
dc.identifierhttp://arxiv.org/abs/math/0702174
dc.identifierAnnals of Global Analysis and Geometry 33, 3 (2008) 293-306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157602
dc.subjectDifferential Geometry
dc.subject53A07, 53C20, 53C21, 58C40
dc.titlePinching of the First Eigenvalue of the Laplacian and almost-Einstein Hypersurfaces of the Euclidean Space
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