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Holomorphic realizations of pairs of foliations on Riemann surfaces
Let $X$ be a hyperbolic Riemann surface and let $μ$ and $ν$ be laminations on $X$ homotopic to measured foliations with finite Dirichlet integral. We prove that $μ$ and $ν$ are filling if and only if there exists a homeomorphism to another Riemann surface $f:X\to Y$ and an integrable holomorphic qua
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