On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

• Autorzy: Luigi Ambrosio , Jérôme Bertrand
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Alexandrov spaces; surfaces with bounded integral curvature; potential theory on surfaces

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-03-09

zaakceptowano

2016-10-21

online

2016-11-10

Twórcy

autor

Luigi Ambrosio

• Scuola Normale Superiore, Piazza dei Cavalieri 7 56126 Pisa, Italy

autor

Jérôme Bertrand

• Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Toulouse III, 31062 Toulouse cedex 9, France

Identyfikatory

DOI

10.1515/agms-2016-0012