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Shadow lemma on Finsler manifolds of hyperbolic type. (English) Zbl 1404.58051

Summary: Let \((M, F)\) be a compact Finsler manifold of hyperbolic type, \(\tilde{M}_F\) be its universal Finslerian covering and \(\alpha^F\) the critical exponent of the group of the deck transformations of \(\tilde{M}_F\). In this paper we prove the existence of an \(\alpha^F\)-Busemann quasi-density on the Gromov boundary \(\tilde{M}_F^G(\infty)\) of \(\tilde{M}_F\). Furthermore, we generalize the Shadow lemma to the compact Finsler manifolds of hyperbolic type.

MSC:

58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
35B33 Critical exponents in context of PDEs
30F25 Ideal boundary theory for Riemann surfaces
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