# 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

, Volume 3 (2) – May 1, 2001
33 pages      /lp/springer-journals/the-cr-yamabe-conjecture-the-case-n-1-E94ugi5S7m
Publisher
Springer Journals
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 SocietySpringer Journals

Published: May 1, 2001