Vol. 4, No. 2, 2022

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Harmonic quasi-isometries of pinched Hadamard surfaces are injective

Yves Benoist and Dominique Hulin

Vol. 4 (2022), No. 2, 307–328
Abstract

We prove that a harmonic quasi-isometric map between pinched Hadamard surfaces is a quasi-conformal diffeomorphism.

Keywords
harmonic map, quasi-isometric map, boundary map, negative curvature, quasi-conformal diffeomorphism
Mathematical Subject Classification
Primary: 53C43
Secondary: 30C62, 58E20
Milestones
Received: 6 January 2021
Revised: 4 October 2021
Accepted: 22 October 2021
Published: 24 August 2022
Authors
Yves Benoist
Département de Mathématiques
Université Paris-Sud 11
Faculté des Sciences d’Orsay
Orsay
France
Dominique Hulin
Département de Mathématiques
Université Paris-Sud 11
Faculté des Sciences d’Orsay
Orsay
France