Rigidity and dynamics around manifolds of negative curvature
In this survey article, the author discusses results and problems related to several invariant measures for the geodesic flow on the unit tangent bundle of a compact negatively curved Riemannian manifold \(M\). The discussion is centered at the conjecture of Katok and Sullivan that a manifold as above is locally symmetric if the measure classes of any two of the three measures -- visibility, Patterson-Sullivan, or harmonic measure -- on \(\widetilde{M} (\infty)\) coincide.
scientific article; zbMATH DE number 817680