# Morrey’s 𝜖-conformality lemma in metric spaces

• Fitzi, Martin Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700 Fribourg, Switzerland
• Wenger, Stefan Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700 Fribourg, Switzerland
2020
Published in:
• Proceedings of the American Mathematical Society. - 2020, vol. 148, no. 10, p. 4285–4298
English 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.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
• English
Classification
Mathematics