Area minimizing discs in metric spaces
- Lytchak, Alexander Mathematisches InstitutUniversität Köln, Germany
- Wenger, Stefan Department of MathematicsUniversity of Fribourg, Switzerland
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01.03.2017
Published in:
- Archive for Rational Mechanics and Analysis. - 2017, vol. 223, no. 3, p. 1123–1182
English
We solve the classical problem of Plateau in the setting of proper metric spaces. Precisely, we prove that among all disc-type surfaces with prescribed Jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi-conformal parametrization. If the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally Hölder continuous in the interior and continuous up to the boundary. Our results generalize corresponding results of Douglas Radò and Morrey from the setting of Euclidean space and Riemannian manifolds to that of proper metric spaces.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 288684
- DOI 10.1007/s00205-016-1054-3
- Persistent URL
- https://folia.unifr.ch/unifr/documents/305458
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