The universal family of punctured Riemann surfaces is SteinForstnerič, Franc (Avtor) Riemann surfacesTeichmüller spaceuniversal familySteinova manifoldOka manifoldWe 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.20262026-05-21 09:18:17Neznano29489sl