Solving $\bar\partial_b$ on hyperbolic laminations

Details Solving $\bar\partial_b$ on hyperbolic laminations Solving $\bar\partial_b$ on hyperbolic laminations

2011-08-10

arxiv.org/abs/1108.2286v1

Mathematics

Complex Variables

Scientific paper

Let $X$ denote a compact set which is laminated by Riemann surfaces. We assume that $X$ carries a positive CR line bundle $ L\rightarrow X$. The main result of the paper is that there exists a positive integer $s$ so that if $v$ is any continuous $(0,1)$ form with coefficients in $L^{\otimes s}$ there exists a continuous section $u$ of $L^{\otimes s}$ solving the equation $\bar\partial_b u=v$.

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