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Smooth approximation of Lipschitz functions on Finsler manifolds Garrido Carballo, María Isabel Jaramillo Aguado, Jesús Ángel Rangel, Yenny C. 514.7 Riemannian-manifolds isometries Geometría diferencial 1204.04 Geometría Diferencial Supported in partby D.G.I. (Spain) Grant MTM2009-07848. Y. C. Rangel hasbeen associated to the Project 014-CT-2012 (CDCHT-UCLA)(Venezuela) We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon : M -> (0, infinity) and each r > 0, there exists a C-1-smooth Lipschitz function g : M -> R such that vertical bar f(x) - g(x)vertical bar <= epsilon(x), for every x is an element of M, and Lip(g) <= Lip(f) + r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra C-b(1)(M) of all C-1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T : C-b(1)(N) -> C-b(1)(M) as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds. Depto. de Álgebra, Geometría y Topología Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-19T13:22:06Z 2023-06-19T13:22:06Z 2013 journal article https://hdl.handle.net/20.500.14352/33358 0972-6802 10.1155/2013/164571 eng Garrido, M. I., et al. «Smooth Approximation of Lipschitz Functions on Finsler Manifolds». Journal of Function Spaces and Applications, vol. 2013, 2013, pp. 1-10. DOI.org (Crossref), https://doi.org/10.1155/2013/164571 open access application/pdf Hindawi