On the regularity of Alexandrov surfaces with curvature bounded below

Ambrosio Luigi - Bertrand Jerome

year: 2014
journal: Proc. AMS
abstract: In this note, we prove that the distance of a surface with Alexandrov's curvature bounded below derives from a Riemannian metric whose components, for any $p\in [1,2)$, locally belong to $W^{1,p}$ 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.