Geodesic
On the Regularity of Alexandrov Surfaces with Curvature Bounded Below
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : Alexandrov spaces, surfaces with bounded integral curvature, potential theory on surfaces 
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     title = {On the {Regularity} of {Alexandrov} {Surfaces} with {Curvature} {Bounded} {Below}},
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Ambrosio, Luigi; Bertrand, Jérôme. On the Regularity of Alexandrov Surfaces with Curvature Bounded Below. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a15/