Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane H, and let M = Γ\H be the associated finite volume hyperbolic Riemann surface. If γ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If γ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbo...

We prove that any Coxeter group that is not virtually free contains a surface group. In particular if the Coxeter group is word hyperbolic and not virtually free this establishes the existence of a hyperbolic surface group, and answers in the affirmative a question of Gromov in this setting. We also discuss when Artin groups contain hyperbolic surface groups. 2000 Mathematics Subject Classifica...

To illustrate what this paper is about we first consider a classical example of a translation surface. Consider two copies of a regular Euclidean pentagon as on the left of figure 1. Identifying opposite parallel sides by translations one obtains a Riemann surface with a natural locally flat metric with one cone type point of total angle 6π. Since this is a compact Riemann surface it is also an...

We introduce a new unmarked geometric spectrum, the lengthangle spectrum, for closed hyperbolic surfaces. We show that unlike the length spectrum, the length-angle spectrum of any closed hyperbolic surface determines the surface, up to isometry.

the present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). both the half-spaces are assumed to be under compressive initial stress. the study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. the dispersion relation ...

Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group contains a hyperbolic surface group if the free group has rank two, or every generator is used the same number of times in the list of amalgamating words. Our method is based on formulating a stronger conjecture on tilings of closed surfaces combin...

We show that every transitive hyperbolic set on a surface is included in a locally maximal hyperbolic set.