RT Journal Article
T1 Smooth approximation of Lipschitz functions on Riemannian manifolds
A1 Azagra Rueda, Daniel
A1 Ferrera Cuesta, Juan
A1 López-Mesas Colomina, Fernando
A1 Rangel, Y.
AB 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.
PB Elsevier
SN 0022-247X
YR 2007
FD 2007-02-15
LK https://hdl.handle.net/20.500.14352/49817
UL https://hdl.handle.net/20.500.14352/49817
LA eng
DS Docta Complutense
RD 28 abr 2024