On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Luigi Ambrosio, and Jérôme Bertrand. "On the Regularity of Alexandrov Surfaces with Curvature Bounded Below." Analysis and Geometry in Metric Spaces 4.1 (2016): 282-287, electronic only. <http://eudml.org/doc/287063>.

@article{LuigiAmbrosio2016,
abstract = {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.},
author = {Luigi Ambrosio, Jérôme Bertrand},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Alexandrov spaces; surfaces with bounded integral curvature; potential theory on surfaces},
language = {eng},
number = {1},
pages = {282-287, electronic only},
title = {On the Regularity of Alexandrov Surfaces with Curvature Bounded Below},
url = {http://eudml.org/doc/287063},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Luigi Ambrosio
AU - Jérôme Bertrand
TI - On the Regularity of Alexandrov Surfaces with Curvature Bounded Below
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 282
EP - 287, electronic only
AB - 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.
LA - eng
KW - Alexandrov spaces; surfaces with bounded integral curvature; potential theory on surfaces
UR - http://eudml.org/doc/287063
ER -