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
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
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