We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of ...

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the ...

Let H be the hyperbolic space of dimension n + 1. A geodesic foliation of H is given by a smooth unit vector field on L all of whose integral curves are geodesics. Each geodesic foliation of L determines an n-dimensional ...

We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can ...

We consider foliations of the whole three dimensional hyperbolic space H3 by oriented geodesics. Let L be the space of all the oriented geodesics of H3, which is a four dimensional manifold carrying two canonical ...

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that ...

We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of ...

We prove an inequality concerning isometrics of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral ...