We prove the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recently, roughly by extending the problem across the boundary of the compactificat...

Abstract We provide optimal bounds for the sine and hyperbolic tangent means in terms of various weighted arithmetic centroidal

A.1. Slow Slip Episodes In this section, we discuss the relevant information for identification of slow slip episodes, with additional details presented elsewhere (Holtkamp et al., 2006, ms. in prep.). The GPS data analyzed for slow slip episodes is from the PANGA network provided by the Central Washington University clearinghouse (2005). PANGA time series are network solutions with phase ambig...

Tangent measure distributions were introduced by Bandt 2] and Graf 8] as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by certain contractive mappings, which are not necessarily similitudes. We show that the tangent measure distributions o...

We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and nite-volume surfaces to this class of in nite-volume hyperbolic manifolds.

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the Laplacian. In the hyperbolic near infinity case the d...

In [Z1] S. Zelditch introduced an equivariant version of a pseudo-differential calculus on a hyperbolic Riemann surface. We recast his construction in terms of trilinear invariant functionals on irreducible unitary representations of PGL2(R). This allows us to use certain properties of these functionals in the study of the action of pseudodifferential operators on eigenfunctions of the Laplacia...

In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...