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Runge and Mergelyan theorems on families of open Riemann surfaces
Given a smooth open oriented surface \(X\), endowed with a family of complex structures \(\{J_b\}_{b\in B}\) of some Hölder class and depending continuously or smoothly on the parameter \(b\) in a suitable topological space \(B\), we construct continuous or smooth families \(F_b:X\to Y\), \(b\in B\)
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