This book presents the foundations of the theory of groups and semigroups acting
isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the …

A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $
n $-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of …

We classify the minimum-volume smooth complex hyperbolic surfaces that admit smooth
toroidal compactifications, and we explicitly construct their compactifications. There are five …

In this article, for any $ n\geq 4$ we construct a sequence of compact hyperbolic $ n $-
manifolds $\{M_i\} $ with number of systoles at least as $\mathrm {vol}(M_i)^{1+\frac {1}{3n …

This is a survey of the impact of Thurston's work on knot theory, laying emphasis on the two
characteristic features, rigidity and flexibility, of 3-dimensional hyperbolic structures. We also …

We show that for a closed hyperbolic 3‐manifold, the size of the first eigenvalue of the
Hodge Laplacian acting on coexact 1‐forms is comparable to an isoperimetric ratio relating …

We prove that $\operatorname {vol}(S^{d})/8$ is the highest volume of a pair of $ d $-
dimensional isospectral and non-isometric spherical orbifolds for any $ d\geq5 …

A fake quadric is a smooth projective surface that has the same rational cohomology as a
smooth quadric surface but is not biholomorphic to one. We provide an explicit classification …

In this thesis we study the topology of closed hyperbolizable manifolds with bounded
diameter and bounded volume entropy. We prove that their fundamental group contains free …

Let M be a compact hyperbolic n–dimensional manifold with nonempty totally geodesic
boundary. An orthogeodesic of M is a geodesic arc with endpoints in@ M which are …