Closed holomorphic 1-forms without zeros on Stein manifolds

Universal Locally Univalent Functions and Universal Conformal Metrics with Constant Curvature

“…Then there exists a sequence (f m ) ⊆ H =0 (Ω) such that lim m→∞ f m = g uniformly on K and Remark 3.3. Theorem 3.2 is in fact a special case of Theorem 2 in [23], where closed holomorphic 1-forms on Stein manifolds are considered. We give a direct and simpler proof for the one-dimensional situation of Theorem 3.2.…”

“…Note that it is already a deep result due to Gunning and Narasimhan [17] that every open Riemann surface carries at least one locally univalent holomorphic function. Recently, Frostnerič [10] extended the Gunning-Narasimhan theorem to Stein manifolds and Majcen [23] established a Runge-type theorem for holomorphic 1-forms on Stein manifolds. We shall use some of the ideas of these papers in our proof of Theorem 1.1.…”