Shadow lemma on Finsler manifolds of Sciences hyperbolic type

Abstract

Abstract. Let (M, F ) be a compact Finsler manifold of hyperbolic type, M̃ F be its universal Finslerian covering and α F the critical exponent of the group of the deck transformations of M̃ F . In this paper we prove the existence of an α F -Busemann quasi-density on the Gromov boundary M̃ F G (∞) of M̃ F . Fur- thermore, we generalize the Shadow lemma to the compact Finsler manifolds of hyperbolic type.