SHADOW LEMMA ON FINSLER MANIFOLDS OF HYPERBOLIC TYPE

Abstract

Let (M, F ) be a compact Finsler manifold of hyperbolic type, ˜MFbe its universal Finslerian covering and αFthe critical exponent of the groupof the deck transformations of ˜F. In this paper we prove the existence of anαF-Busemann quasi-density on the Gromov boundary ˜MG(∞) of ˜. Furthermore, we generalize the Shadow lemma to the compact Finsler manifoldsof hyperbolic type