Journal article

Maximal metric surfaces and the Sobolev-to-Lipschitz property

  • Creutz, Paul University of Cologne, Weyertal 86-90, 50931, Cologne, Germany
  • Soultanis, Elefterios University of Fribourg, Chemin du Musee 23, CH-1700, Fribourg, Switzerland
    20.09.2020
Published in:
  • Calculus of Variations and Partial Differential Equations. - 2020, vol. 59, no. 5, p. 177
English We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak–Wenger, which satisfies a related maximality condition.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/309202
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