Controlled Geometry via Smoothing

Peter Petersen, Guofang Wei, R. Ye

Type: Article

Publication Date: 1999-09-30

Citations: 22

DOI: https://doi.org/10.1007/s000140050093

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.

Locations

Commentarii Mathematici Helvetici - View - PDF
arXiv (Cornell University) - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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