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July 2021 Harmonic quasi-isometric maps into Gromov hyperbolic $\operatorname{CAT}(0)$-spaces
Hubert Sidler, Stefan Wenger
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J. Differential Geom. 118(3): 555-572 (July 2021). DOI: 10.4310/jdg/1625860625

Abstract

We show that for every quasi-isometric map from a Hadamard manifold of pinched negative curvature to a proper, Gromov hyperbolic, $\operatorname{CAT}(0)$-space there exists an energy minimizing harmonic map at finite distance. This harmonic map is moreover Lipschitz. This generalizes a recent result of Benoist–Hulin.

Funding Statement

Research partially funded by Swiss National Science Foundation Grants 165848 and 182423.

Citation

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Hubert Sidler. Stefan Wenger. "Harmonic quasi-isometric maps into Gromov hyperbolic $\operatorname{CAT}(0)$-spaces." J. Differential Geom. 118 (3) 555 - 572, July 2021. https://doi.org/10.4310/jdg/1625860625

Information

Received: 7 May 2018; Accepted: 18 June 2019; Published: July 2021
First available in Project Euclid: 10 July 2021

Digital Object Identifier: 10.4310/jdg/1625860625

Subjects:
Primary: 53C23, 53C43, 58E20

Rights: Copyright © 2021 Lehigh University

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Vol.118 • No. 3 • July 2021
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