Controlled Geometry via Smoothing

Details Controlled Geometry via Smoothing Controlled Geometry via Smoothing

1995-08-23

arxiv.org/abs/dg-ga/9508012v1

Mathematics

Differential Geometry

18 pages, Latex

Scientific paper

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.

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