Smooth approximation of Lipschitz functions on Riemannian manifolds



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Azagra Rueda, Daniel and Ferrera Cuesta, Juan and López-Mesas Colomina, Fernando and Rangel, Y. (2007) Smooth approximation of Lipschitz functions on Riemannian manifolds. Journal of Mathematical Analysis and Applications, 326 (2). pp. 1370-1378. ISSN 0022-247X

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We show that for every Lipschitz function f defined on a separable Riemannian manifold M (possibly of infinite dimension), for every continuous epsilon : M -> (0, + infinity), and for every positive number r > 0, there exists a C-infinity smooth Lipschitz function g : M -> R such that vertical bar f(p) - g(p)vertical bar <= epsilon(p) for every p is an element of 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.

Item Type:Article
Uncontrolled Keywords:Lipschitz function; Riemannian manifold; Smooth approximation; Hamilton-Jacobi equations; convex functions; spaces
Subjects:Sciences > Mathematics > Differential geometry
ID Code:14761
Deposited On:17 Apr 2012 11:44
Last Modified:06 Aug 2018 10:25

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