Universität zu Köln

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

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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:	Creators Email ORCID ORCID Put Code Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Wenger, Stefan UNSPECIFIED orcid.org/0000-0003-3645-105X UNSPECIFIED
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:	Keywords Language VALUED FUNCTIONS; PLATEAU-PROBLEM; CURRENTS; REGULARITY; SOBOLEV Multiple languages Mathematics, Applied; Mechanics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/23868