Smooth approximation of Lipschitz functions on Riemannian manifolds |
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Authors: | D. Azagra J. Ferrera Y. Rangel |
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Affiliation: | Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain |
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Abstract: | We show that for every Lipschitz function f defined on a separable Riemannian manifold M (possibly of infinite dimension), for every continuous , and for every positive number r>0, there exists a C∞ smooth Lipschitz function such that |f(p)−g(p)|?ε(p) for every p∈M and Lip(g)?Lip(f)+r. Consequently, every separable Riemannian manifold is uniformly bumpable. We also present some applications of this result, such as a general version for separable Riemannian manifolds of Deville-Godefroy-Zizler's smooth variational principle. |
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Keywords: | Lipschitz function Riemannian manifold Smooth approximation |
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