Morrey’s 𝜖-conformality lemma in metric spaces

Fitzi, Martin; Wenger, Stefan

doi:10.1090/proc/15065

Morrey’s $\varepsilon$-conformality lemma in metric spaces
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Proc. Amer. Math. Soc. 148 (2020), 4285-4298 Request permission

Abstract:

We provide a simpler proof and slight strengthening of Morrey’s famous lemma on $\varepsilon$-conformal mappings. Our result more generally applies to Sobolev maps with values in a complete metric space, and we obtain applications to the existence of area minimizing surfaces of higher genus in metric spaces. Unlike Morrey’s proof, which relies on the measurable Riemann mapping theorem, we only need the existence of smooth isothermal coordinates established by Korn and Lichtenstein.

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