We prove new upper bounds for the first positive eigenvalue of a family of second order operators, including the Bakry-Émery Laplacian, for submanifolds of weighted Euclidean spaces.
Robert C. Reilly a obtenu des majorations de la première valeur propre du laplacien pour les hypersurfaces de l’espace euclidien. De plus, il a montré que le cas d’égalité dans ces majorations est atteint uniquement pour les sphères géodésiques. Dans cet exposé, nous nous intéressons au problème de pincement pour ces majorations. Nous montrons que si le cas d’égalité est presque atteint, alors l’hypersurface est proche d’une sphère, en un sens que nous préciserons. Nous déduisons ensuite des résultats...
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the -sense is -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [] and [].
We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.
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