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arXiv · 1701.06346

Canonical parametrizations of metric discs

Alexander Lytchak·Stefan Wenger
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Abstract

We use the recently established existence and regularity of area and energy minimizing discs in metric spaces to obtain canonical parametrizations 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 parametrizations 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. 2017-01-23. Canonical parametrizations of metric discs. https://doi.org/10.1215/00127094-2019-0065

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