Regularity of harmonic discs in spaces with quadratic isoperimetric inequality



We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs.

Mathematics Subject Classification

Primary 58E20 Secondary 49N60 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität KölnCologneGermany
  2. 2.Department of MathematicsUniversity of FribourgFribourgSwitzerland

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