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P. Bérard et D. Meyer ont démontré une inégalité du type Faber-Krahn pour les domaines
d'une variété compacte à courbure de Ricci positive. Nous démontrons des résultats de
stabilité associés à cette inégalité.
In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
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