20.500.12556/DiRROS-29489 The universal family of punctured Riemann surfaces is Stein We show that the universal Teichmüller family $V(g, n)$ of compact Riemann surfaces of genus $g \ge 0$ with $n > 0$ punctures is a Stein manifold. We describe its basic function-theoretic properties and pose some challenging questions. We show, in particular, that the space of fibrewise algebraic functions on the universal family is dense in the space of holomorphic functions, and that there is a fibrewise algebraic map of the universal family to a Euclidean space which restricts to a proper embedding on any fibre. We also obtain a relative Oka principle for holomorphic fibrewise algebraic maps of the universal family to any flexible algebraic manifold. Riemann surfaces Teichmüller space universal family Steinova manifold Oka manifold Riemannove ploskve Teichmüllerjev prostor univerzalna družina Steinova mnogoterost Oka mnogoterost true false true Angleški jezik Slovenski jezik Neznano 2026-05-21 09:18:17 2026-05-21 09:18:17 2026-05-22 03:48:48 0000-00-00 00:00:00 2026 0 0 16 str. iss. 5, article no. e70383 Vol. 58 May 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-05-01 517.5 0024-6093 10.1112/blms.70383 278869507 Bulletin_of_London_Math_Soc_-_2026_-_Forstneric_-_The_universal_family_of_punctured_Riemann_surfaces_is_Stein.pdf Bulletin_of_London_Math_Soc_-_2026_-_Forstneric_-_The_universal_family_of_punctured_Riemann_surfaces_is_Stein.pdf 1 9AEF4EC70E89B2E05A6C7F34BBA7BDF5 f7a990a5ab096d7f8c887c6681d8a796322b8487d7f929d147052873c4e81620 bef20934-54e5-11f1-8a5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44241 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70383 1 3ddf51a9-54e5-11f1-8a5a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44240 Inštitut za matematiko, fiziko in mehaniko 0 0 0