Smooth approximation of lipschitz functions on finsler manifolds


Abstract:

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 ε: M → (0, ∞) and each r > 0, there exists a C 1 -smooth Lipschitz function g: M → R such that | f (x) - g (x) | ≤ ε (x), for every x ∈ M, and L i p (g) ≤ L i p (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. © 2013 M. I. Garrido et al.

Año de publicación:

2013

Keywords:

    Fuente:

    scopusscopus
    googlegoogle

    Tipo de documento:

    Article

    Estado:

    Acceso abierto

    Áreas de conocimiento:

    • Modelo matemático
    • Optimización matemática

    Áreas temáticas:

    • Topología
    • Análisis
    • Geometría