Lytchak, Alexander and Wenger, Stefan ORCID: 0000-0003-3645-105X
(2017).
Area Minimizing Discs in Metric Spaces.
Arch. Ration. Mech. Anal., 223 (3).
S. 1123 - 1183.
NEW YORK:
SPRINGER.
ISSN 1432-0673
Abstract
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 Holder continuous in the interior and continuous up to the boundary. Our results generalize corresponding results of Douglas Rad and Morrey from the setting of Euclidean space and Riemannian manifolds to that of proper metric spaces.
Item Type: | Journal Article | ||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-238680 | ||||||||||||
DOI: | 10.1007/s00205-016-1054-3 | ||||||||||||
Journal or Publication Title: | Arch. Ration. Mech. Anal. | ||||||||||||
Volume: | 223 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | S. 1123 - 1183 | ||||||||||||
Date: | 2017 | ||||||||||||
Publisher: | SPRINGER | ||||||||||||
Place of Publication: | NEW YORK | ||||||||||||
ISSN: | 1432-0673 | ||||||||||||
Language: | English | ||||||||||||
Faculty: | Faculty of Mathematics and Natural Sciences | ||||||||||||
Divisions: | Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute | ||||||||||||
Subjects: | no entry | ||||||||||||
Uncontrolled Keywords: |
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Refereed: | Yes | ||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/23868 |
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