The notion of Gromov hyperbolicity was introduced by Gromov in the setting of geometric group theory [G1], [G2], but has played an increasing role in analysis on general metric spaces [BHK], [BS], [BBo], [BBu], and extendability of Lipschitz mappings [L]. In this theory, it is often additionally assumed that the hyperbolic metric space is proper and geodesic (meaning that closed balls are compa...

We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and the stable manifold of one of these saddles coincides with the strongly stable leaf, then it does not satisfy the specification property.

Abstract We show that if the automorphism group of a projective variety is torsion, then it finite. Motivated by Lang’s conjecture on rational points hyperbolic varieties, we use this to prove with only finitely many has automorphisms. Moreover, investigate what extent finiteness S -integral over number field persists generated fields. To end, introduce class mildly bounded varieties and genera...

Let G G be a finitely presented group, and let H"> H encoding="application/x-tex">H subgroup of </inl...