Universität zu Köln

Creutz, Paul and Soultanis, Elefterios (2020). Maximal metric surfaces and the Sobolev-to-Lipschitz property. Calc. Var. Partial Differ. Equ., 59 (5). HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-0835

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Abstract

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak-Wenger, which satisfies a related maximality condition.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Creutz, Paul UNSPECIFIED UNSPECIFIED UNSPECIFIED Soultanis, Elefterios UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-318781
DOI:	10.1007/s00526-020-01843-0
Journal or Publication Title:	Calc. Var. Partial Differ. Equ.
Volume:	59
Number:	5
Date:	2020
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-0835
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUASI-SYMMETRIC PARAMETRIZATIONS; INFINITY-POINCARE INEQUALITY; VOLUME RIGIDITY; SPACES Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/31878