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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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X0600343X

## Abstract

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 |
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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 Feb 2014 10:08 |

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