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15 March 2020 Canonical parameterizations of metric disks
Alexander Lytchak, Stefan Wenger
Duke Math. J. 169(4): 761-797 (15 March 2020). DOI: 10.1215/00127094-2019-0065

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.

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Alexander Lytchak. Stefan Wenger. "Canonical parameterizations of metric disks." Duke Math. J. 169 (4) 761 - 797, 15 March 2020. https://doi.org/10.1215/00127094-2019-0065

Information

Received: 15 November 2017; Revised: 16 July 2019; Published: 15 March 2020
First available in Project Euclid: 6 February 2020

zbMATH: 07198465
MathSciNet: MR4073230
Digital Object Identifier: 10.1215/00127094-2019-0065

Subjects:
Primary: 30L10
Secondary: 30C65, 49Q05, 58E20

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 4 • 15 March 2020
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