Universität zu Köln

Lytchak, Alexander and Wenger, Stefan ORCID: 0000-0003-3645-105X (2020). CANONICAL PARAMETERIZATIONS OF METRIC DISKS. Duke Math. J., 169 (4). S. 761 - 798. DURHAM: DUKE UNIV PRESS. ISSN 1547-7398

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Abstract

We use the recently established existence and regularity of area and energy minimizing disks in metric spaces to obtain canonical parameterizations of metric surfaces. Our approach yields a new and conceptually simple proof of a well-known theorem of Bonk and Kleiner on the existence of quasisymmetric parameterizations of linearly locally connected, Ahlfors 2-regular metric 2-spheres. Generalizations and applications to the geometry of such surfaces are described.

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:38-340939
DOI:	10.1215/00127094-2019-0065
Journal or Publication Title:	Duke Math. J.
Volume:	169
Number:	4
Page Range:	S. 761 - 798
Date:	2020
Publisher:	DUKE UNIV PRESS
Place of Publication:	DURHAM
ISSN:	1547-7398
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 QUASI-SYMMETRIC PARAMETRIZATIONS; SOBOLEV SPACES; HARMONIC MAPS; DIMENSION Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/34093