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Let $X$ be a Cartan-Hadamard manifold, meaning a complete, connected, simply connected Riemannian manifold with non-positive sectional curvature and $\Gamma < Isom(X)$ a discrete group of ...

Birman and Series in their article GEODESICS WITH BOUNDED INTERSECTION NUMBER ON SURFACES ARE SPARSELY DISTRIBUTED proved that the set of points on a hyperbolic surface (possibly with boundary) ...

Let $X$ be a hyperbolic manifold of finite volume. I want to prove that $X$ has ends of the form $N\times \mathbb{R}$ where $N$ has a finite covering by a nilmanifold and $\pi_1N\to \pi_1 X$ is ...