Quasi-Fuchsian vs Negative curvature metrics on surface groups

Ethan Fricker; Alex Furman

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arXiv · 2108.07947

Quasi-Fuchsian vs Negative curvature metrics on surface groups

Ethan Fricker·Alex Furman

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Abstract

We compare two families of left-invariant metrics on a surface group $\Gamma=\pi_1(\Sigma)$ in the context of course-geometry. One family comes from Riemannian metrics of negative curvature on the the surface $\Sigma$, and another from quasi-Fuchsian representations of $\Gamma$. We show that the Teichmuller space $\Teich(\Sigma)$ is the only common part of these two families, even when viewed from the coarse-geometric perspective.

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Ethan Fricker, Alex Furman. 2021-08-18. Quasi-Fuchsian vs Negative curvature metrics on surface groups. https://arxiv.org/abs/2108.07947

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