Controlled Geometry via Smoothing |
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| Authors: | P Petersen G Wei R Ye |
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| Institution: | (1) Department of Mathematics, UCLA, Los Angeles, CA 90095, USA, e-mail: petersen@math.ucla.edu, US;(2) Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, e-mail: wei@math.ucsb.edu and yer@math.ucsb.edu, US |
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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.
Received: August 31, 1995. |
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| Keywords: | , Smoothing, regularity of metric, curvature bounds, |
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