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The CR Yamabe conjecture the case n = 1

The CR Yamabe conjecture the case n = 1 Let (M,θ) be a compact CR manifold of dimension 2n+1 with a contact form θ, and L=(2+2/n)Δ b +R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form &θtilde; on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that¶ ¶D. Jerison and J.M. Lee solved the CR Yamabe problem in the case where n≥2 and (M,θ) is not locally CR equivalent to the sphere S 2n+1 of C n . In a join work with R. Yacoub, the CR Yamabe problem was solved for the case where (M,θ) is locally CR equivalent to the sphere S 2n+1 for all n. In the present paper, we study the case n=1, left by D. Jerison and J.M. Lee, which completes the resolution of the CR Yamabe conjecture for all dimensions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

The CR Yamabe conjecture the case n = 1

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/PL00011303
Publisher site
See Article on Publisher Site

Abstract

Let (M,θ) be a compact CR manifold of dimension 2n+1 with a contact form θ, and L=(2+2/n)Δ b +R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form &θtilde; on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that¶ ¶D. Jerison and J.M. Lee solved the CR Yamabe problem in the case where n≥2 and (M,θ) is not locally CR equivalent to the sphere S 2n+1 of C n . In a join work with R. Yacoub, the CR Yamabe problem was solved for the case where (M,θ) is locally CR equivalent to the sphere S 2n+1 for all n. In the present paper, we study the case n=1, left by D. Jerison and J.M. Lee, which completes the resolution of the CR Yamabe conjecture for all dimensions.

Journal

Journal of the European Mathematical Society – Springer Journals

Published: May 1, 2001

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