Harmonic quasi-isometric maps into Gromov hyperbolic ${\rm CAT}(0)$-spaces

Hubert Sidler; Stefan Wenger

arxiv: 1804.06286 · v1 · pith:SZIHNGPPnew · submitted 2018-04-17 · 🧮 math.DG · math.MG

Harmonic quasi-isometric maps into Gromov hyperbolic {rm CAT}(0)-spaces

Hubert Sidler , Stefan Wenger This is my paper

classification 🧮 math.DG math.MG

keywords harmonicgromovhyperbolicquasi-isometricbenoist-hulincompactcurvaturedistance

0 comments

read the original abstract

We show that for every quasi-isometric map from a Hadamard manifold of pinched negative curvature to a locally compact, Gromov hyperbolic, ${\rm CAT}(0)$-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.

This paper has not been read by Pith yet.

Harmonic quasi-isometric maps into Gromov hyperbolic {rm CAT}(0)-spaces

discussion (0)