The Huber theorem for non-compact conformally flat manifolds |
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Authors: | G Carron M Herzlich |
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Institution: | Département de Mathématiques, CNRS UMR 6629, Université de Nantes, Case postale 92208, F-44322 Nantes-Cedex 3, France, e-mail: Gilles.Carron@math.univ-nantes.fr, FR Département de Mathématiques, CNRS UMR 5030, Université Montpellier II, case 51,? F-34095 Montpellier-Cedex 5, France, e-mail: herzlich@math.univ-montp2.fr, FR
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Abstract: | It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact
surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened
in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold
with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled
from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together
with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions.
Received: April 14, 2000; revised version: March 20, 2001 |
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Keywords: | , Non compact Riemannian manifolds, Ricci curvature, conformal geometry, compactification, asymptotically locally,,,,,euclidean manifolds, |
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