| Title: | Runge and Mergelyan theorems on families of open Riemann surfaces |
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| Authors: | ID Forstnerič, Franc (Author) |
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| Files: |  PDF - Presentation file, download (2,51 MB)
MD5: 17E6B77384E6F6ECA19FBA024E3045AF
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870826003580
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | Riemann surfaces, Runge theorem, Mergelyan theorem, Oka manifold, Stein manifold, minimal surfaces |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.10.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 58 str. |
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| Numbering: | Vol. 502, part B, article no. 111137 |
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| PID: | 20.500.12556/DiRROS-31290  |
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| UDC: | 517.5 |
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| ISSN on article: | 0001-8708 |
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| DOI: | 10.1016/j.aim.2026.111137 |
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| COBISS.SI-ID: | 285931523 |
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| Publication date in DiRROS: | 24.07.2026 |
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| Views: | 145 |
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| Downloads: | 148 |
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