Controlled Geometry via Smoothing
dg-ga
2008-02-03 v1 Differential Geometry
Abstract
We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a generalization of Gromov's almost flat manifold theorem. A uniform Betti number estimate is also obtained.
Cite
@article{arxiv.dg-ga/9508012,
title = {Controlled Geometry via Smoothing},
author = {Peter Petersen and Guofang Wei and Rugang Ye},
journal= {arXiv preprint arXiv:dg-ga/9508012},
year = {2008}
}
Comments
18 pages, Latex