Atindogbé, Cyriaque; Ogouyandjou, Carlos; Tossa, Joël Shadow lemma on Finsler manifolds of hyperbolic type. (English) Zbl 1404.58051 Math. Sci. Appl. E-Notes 2, No. 2, 76-88 (2014). 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. Cited in 1 Document 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 Keywords:Finsler manifold; Gromov hyperbolic manifold; Busemann quasidensity; shadow lemma PDFBibTeX XMLCite \textit{C. Atindogbé} et al., Math. Sci. Appl. E-Notes 2, No. 2, 76--88 (2014; Zbl 1404.58051)