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I'm reading about the Mostow's rigidity theorem, and the proof uses the following (maybe well-known) result: The geodesic flow on a manifold with negative curvature is ergodic. The lecture note that ...

Consider a compact surface $M$ of genus $g \geq 2$ with a metric of constant negative curvature. My question is, is it known under what sorts of sufficient conditions such a metric will have non-...

I am looking for a reference to a proof of the following well-know fact (cited for example by B.Farb in ``Relatively hyperbolic groups'', Geom. Funct. Anal. 8 (1998), no. 5, 810--840); MR1650094, ...