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18 papers · 1 filter
Meromorphic extensions from small families of circles and holomorphic extensions from spheres
Josip Globevnik
Let B be the open unit ball in C^2 and let a, b, c be three points in C^2 which do not lie in a complex line, such that the complex line through a and b meets B and such that <a|b>…
Analyticity of functions analytic on circles
Josip Globevnik
Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and ce…
On meromorphic extendibility
Josip Globevnik
Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on…
Bordered Riemann surfaces in C^2
Franc Forstneric, Erlend Fornaess Wold
One of the oldest open problems in the classical function theory is whether every open Riemann surface admits a proper holomorphic embedding into C^2. In this paper we prove the fo…
Closed holomorphic 1-forms without zeros on Stein Manifolds
Irena Majcen
We prove that a Stein manifold admits a closed holomorphic 1-form without zeros in every class of the first cohomology group. We also prove an approximation result for closed holom…
Approximation of holomorphic mappings on strongly pseudoconvex domains
Barbara Drinovec Drnovsek, Franc Forstneric
Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps fro…