Quasi-Fuchsian vs Negative curvature metrics on surface groups

2021/08/18 by Fricker, Ethan, Furman, Alex
#51F30 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2108.07947

Abstract

We compare two families of left-invariant metrics on a surface group Γ=π₁(Σ) in the context of course-geometry. One family comes from Riemannian metrics of negative curvature on the the surface Σ, and another from quasi-Fuchsian representations of Γ. We show that the Teichmuller space \Teich(Σ) is the only common part of these two families, even when viewed from the coarse-geometric perspective.

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