Lytchak, Alexander and Wenger, Stefan ORCID: 0000-0003-3645-105X
(2017).
Energy and area minimizers in metric spaces.
Adv. Calc. Var., 10 (4).
S. 407 - 422.
BERLIN:
WALTER DE GRUYTER GMBH.
ISSN 1864-8266
Abstract
We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area has been chosen appropriately. We prove the quasi-convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Holder exponents of some area-minimizing discs.
Item Type: | Journal Article | ||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-216139 | ||||||||||||
DOI: | 10.1515/acv-2015-0027 | ||||||||||||
Journal or Publication Title: | Adv. Calc. Var. | ||||||||||||
Volume: | 10 | ||||||||||||
Number: | 4 | ||||||||||||
Page Range: | S. 407 - 422 | ||||||||||||
Date: | 2017 | ||||||||||||
Publisher: | WALTER DE GRUYTER GMBH | ||||||||||||
Place of Publication: | BERLIN | ||||||||||||
ISSN: | 1864-8266 | ||||||||||||
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/21613 |
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