Controlled geometry via smoothing

Authors
Petersen, P Wei, GF Ye, RG
Citation
P. Petersen et al., Controlled geometry via smoothing, COMM MATH H, 74(3), 1999, pp. 345-363
Citations number
21
Categorie Soggetti
Mathematics
Journal title
COMMENTARII MATHEMATICI HELVETICI
ISSN journal
00102571 → ACNP
Volume
74
Issue
3
Year of publication
1999
Pages
345 - 363
Database
ISI
SICI code
0010-2571(1999)74:3<345:CGVS>2.0.ZU;2-3
Abstract
We prove that Riemannian metrics with a uniform weak norm can be smoothed t o having arbitrarily high regularity. This generalizes all previous smoothi ng results. As a consequence we obtain a generalization of Gromov's almost flat manifold theorem. A uniform Betti number estimate is also obtained. Ma thematics Subject Classification (1991). 53C20.