# On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Luigi Ambrosio; Jérôme Bertrand

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 282-287, electronic only
- ISSN: 2299-3274

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topLuigi 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 -

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