20.500.12556/DiRROS-31290 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 $F_b:X\to Y$, $b\in B$ of $J_b$-holomorphic maps to any Oka manifold $Y$, with approximation on a suitable family of compact Runge sets in $X$. Along the way, we prove Runge and Mergelyan approximation theorems and Weierstrass interpolation theorem for functions on such families. We include applications to the construction of families of directed holomorphic immersions and conformal minimal immersions to Euclidean spaces. Riemann surfaces Runge theorem Mergelyan theorem Oka manifold Stein manifold minimal surfaces Riemannove ploskve Rungejev izrek Mergelyanov izrek Oka mnogoterost Steinova mnogoterost minimalne ploskve true false true Angleški jezik Slovenski jezik Neznano 2026-07-24 09:39:12 2026-07-24 09:39:12 2026-07-25 03:45:58 0000-00-00 00:00:00 2026 0 0 58 str. part B, article no. 111137 Vol. 502 Oct. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-10-01 517.5 0001-8708 10.1016/j.aim.2026.111137 285931523 1-s2.0-S0001870826003580-main.pdf 1-s2.0-S0001870826003580-main.pdf 1 17E6B77384E6F6ECA19FBA024E3045AF 2a2320533657f283d808fb100490c9d717d6daac5abeb1c2c93602c5dbd6eb01 2a7cab45-8733-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48357 https://www.sciencedirect.com/science/article/pii/S0001870826003580 1 c4bb1da9-8732-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48356 Inštitut za matematiko, fiziko in mehaniko 0 0 0