On the spectrum of a finite-volume negatively-curved manifold

On the Spectrum of a Finite-volume Negatively-curved Manifold

We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently collapsed, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume manifold with pinched negative sectional curvature, we show that the essential spectrum of the p-form Laplacian is the union of the essential spectra of a collection of ordinary diff...

On the Fundamental Groups of Negatively Curved Manifolds with Finite Volume

We will prove that if M is a complete, simply connected riemannian manifold with sectional curvature K, a < K < 0, for a > 0 and T a properly discontinuous group of isometries of M acting freely on M with volume (M/T) finite, then M/T is compact if and only if T consists of hyperbolic elements.

The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible

For a smooth manifold M we define the Teichmüller space T (M) of all Riemannian metrics on M and the Teichmüller space T ǫ(M) of ǫ-pinched negatively curved metrics on M , where 0 ≤ ǫ ≤ ∞. We prove that if M is hyperbolic the natural inclusion T ǫ(M) →֒ T (M) is, in general, not homotopically trivial. In particular, T ǫ(M) is, in general, not contractible. Section 0. Introduction. Let M be a clo...

On Quasi-Invariant Transverse Measures for the Horospherical Foliation of a Negatively Curved Manifold

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold.

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures,...