Harmonic quasi-isometries of pinched Hadamard surfaces are injective

DOI10.2140/TUNIS.2022.4.307zbMath1503.53129arXiv2012.08307OpenAlexW3112047790WikidataQ114045221 ScholiaQ114045221MaRDI QIDQ2674617

Yves Benoist, Dominique Hulin

Publication date: 14 September 2022

Published in: Tunisian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.08307

zbMATH Keywords

harmonic mapnegative curvatureboundary mapquasi-isometric mapquasi-conformal diffeomorphism

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Quasiconformal mappings in the complex plane (30C62)

Cites Work

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• Conformal autosimilarity
• On certain nonlinear elliptic differential equations and univalent mappings
• The Teichmüller theory of harmonic maps
• Constant mean curvature surface, harmonic maps, and universal Teichmüller space
• On univalent harmonic maps between surfaces
• Elliptic partial differential equations of second order
• Non-univalent harmonic maps homotopic to diffeomorphisms.
• The heat equation and harmonic maps of complete manifolds
• Harmonic quasi-isometric maps. II: Negatively curved manifolds
• Harmonic quasi-isometric maps between rank one symmetric spaces
• Harmonic maps and the Schoen conjecture
• Riemannian Geometry
• Complete Metrics Conformal to the Hyperbolic Disc
• Harmonic functions on complete riemannian manifolds
• Injectivity can fail for higher-dimensional harmonic extensions
• Notions of convexity

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