The CR Yamabe conjecture the case $n=1$

Gamara, Najoua. "The CR Yamabe conjecture the case $n=1$." Journal of the European Mathematical Society 003.2 (2001): 105-137. <http://eudml.org/doc/277441>.

@article{Gamara2001,
abstract = {Let $(M,\theta )$ be a compact CR manifold of dimension $2n+1$ with a contact form $\theta $, and $L=(2+2/n)\Delta _b+R$ its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form $\tilde\{\theta \}$ on $M$ conformal to $\theta $ which has a constant Webster curvature. This problem is equivalent to the existence of a function $u$ such that $Lu=u^\{1+2/n\}$, $u>0$ on $M$. D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where $n\ge 2$ and $(M,\theta )$ is not locally CR equivalent to the sphere $S^\{2n+1\}$ of $\mathbf \{C\}^n$. In a join work with R. Yacoub, the CR Yamabe problem was solved for the case where $(M,\theta )$ 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.},
author = {Gamara, Najoua},
journal = {Journal of the European Mathematical Society},
keywords = {Yamabe conjecture; Yamabe problem; CR manifold; pseudo-Hermitian structure},
language = {eng},
number = {2},
pages = {105-137},
publisher = {European Mathematical Society Publishing House},
title = {The CR Yamabe conjecture the case $n=1$},
url = {http://eudml.org/doc/277441},
volume = {003},
year = {2001},
}

TY - JOUR
AU - Gamara, Najoua
TI - The CR Yamabe conjecture the case $n=1$
JO - Journal of the European Mathematical Society
PY - 2001
PB - European Mathematical Society Publishing House
VL - 003
IS - 2
SP - 105
EP - 137
AB - Let $(M,\theta )$ be a compact CR manifold of dimension $2n+1$ with a contact form $\theta $, and $L=(2+2/n)\Delta _b+R$ its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form $\tilde{\theta }$ on $M$ conformal to $\theta $ which has a constant Webster curvature. This problem is equivalent to the existence of a function $u$ such that $Lu=u^{1+2/n}$, $u>0$ on $M$. D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where $n\ge 2$ and $(M,\theta )$ is not locally CR equivalent to the sphere $S^{2n+1}$ of $\mathbf {C}^n$. In a join work with R. Yacoub, the CR Yamabe problem was solved for the case where $(M,\theta )$ 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.
LA - eng
KW - Yamabe conjecture; Yamabe problem; CR manifold; pseudo-Hermitian structure
UR - http://eudml.org/doc/277441
ER -