ON THE REGULARITY OF ALEXANDROV SURFACES WITH CURVATURE BOUNDED BELOW

Luigi Ambrosio (1) , Jérôme Bertrand (2)

1 SNS - SNS Pisa
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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 W 1,p out of a discrete singular set. This result is based on Reshet-nyak's work on the more general class of surfaces with bounded integral curvature.

Domaines: Géométrie métrique [math.MG]

Luigi Ambrosio, Jérôme Bertrand. ON THE REGULARITY OF ALEXANDROV SURFACES WITH CURVATURE BOUNDED BELOW. Analysis and Geometry in Metric Spaces, 2016. ⟨hal-01967250⟩