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Controlled Geometry via Smoothing

Peter Petersen·Guofang Wei·Rugang Ye
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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.

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Peter Petersen, Guofang Wei, Rugang Ye. 1995-08-23. Controlled Geometry via Smoothing. https://arxiv.org/abs/dg-ga/9508012

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