Universität zu Köln

Lytchak, Alexander and Wenger, Stefan ORCID: 0000-0003-3645-105X (2018). Intrinsic structure of minimal discs in metric spaces. Geom. Topol., 22 (1). S. 591 - 645. COVENTRY: GEOMETRY & TOPOLOGY PUBLICATIONS. ISSN 1364-0380

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Abstract

We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic metric space whose geometric, topological, and analytic properties are controlled by the isoperimetric inequality. Its geometry can be used to control the shapes of all curves and therefore the geometry and topology of the original metric space. The class of spaces arising in this way as intrinsic minimal discs is a natural generalization of the class of Ahlfors regular discs, well-studied in analysis on 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:38-203092
DOI:	10.2140/gt.2018.22.591
Journal or Publication Title:	Geom. Topol.
Volume:	22
Number:	1
Page Range:	S. 591 - 645
Date:	2018
Publisher:	GEOMETRY & TOPOLOGY PUBLICATIONS
Place of Publication:	COVENTRY
ISSN:	1364-0380
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 QUADRATIC ISOPERIMETRIC INEQUALITY; QUASI-SYMMETRIC PARAMETRIZATIONS; SOBOLEV; REGULARITY; SURFACES; VALUES; AREA Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/20309