Harmonic quasi-isometric maps into Gromov hyperbolic ${\rm CAT}(0)$-spaces
Differential Geometry
2018-04-18 v1 Metric Geometry
Abstract
We show that for every quasi-isometric map from a Hadamard manifold of pinched negative curvature to a locally compact, Gromov hyperbolic, -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.
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Cite
@article{arxiv.1804.06286,
title = {Harmonic quasi-isometric maps into Gromov hyperbolic ${\rm CAT}(0)$-spaces},
author = {Hubert Sidler and Stefan Wenger},
journal= {arXiv preprint arXiv:1804.06286},
year = {2018}
}
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14 pages