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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 10, 2016

On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

  • Luigi Ambrosio and Jérôme Bertrand


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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Received: 2016-3-9
Accepted: 2016-10-21
Published Online: 2016-11-10

© 2016 Luigi Ambrosio and Jérôme Bertrand

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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