Universität zu Köln

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

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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:	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:38-216139
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:	Keywords Language Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21613