Smooth Approximation of Lipschitz functions on Riemannian manifolds
| dc.creator | Azagra, D. | |
| dc.creator | Ferrera, J. | |
| dc.creator | Lopez-Mesas, F. | |
| dc.creator | Rangel, Y. | |
| dc.date | 2006-02-02 | |
| dc.date.accessioned | 2026-07-07T07:03:04Z | |
| dc.date.available | 2026-07-07T07:03:04Z | |
| dc.description | We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $ε:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leqε(p)$ for every $p\in M$ and $\textrm{Lip}(g)\leq\textrm{Lip}(f)+r$. 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. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602051 | |
| dc.identifier | http://arxiv.org/abs/math/0602051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108834 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 58E30, 58B20, 46T05, 53C20 | |
| dc.title | Smooth Approximation of Lipschitz functions on Riemannian manifolds | |
| dc.type | text |