# The CR Yamabe conjecture the case $n=1$

Journal of the European Mathematical Society (2001)

- Volume: 003, Issue: 2, page 105-137
- ISSN: 1435-9855

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topGamara, 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 -

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