F. Forstnerič, “Mergelyan's and Arakelian's theorems for manifold-valued maps”, Mosc. Math. J., 2019, Volume 19, Number 3,Pages <nobr>465

This article is cited in 4 papers

Mergelyan's and Arakelian's theorems for manifold-valued maps

F. Forstnerič^ab

^a Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
^b Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

Abstract: In this paper we show that Mergelyan's theorem holds for maps from open Riemann surfaces to Oka manifolds. This is used to prove the analogue of Arakelian's theorem on uniform approximation of holomorphic maps from closed subsets of plane domains to any compact complex homogeneous manifold.

Key words and phrases: Holomorphic map, homogeneous manifold, elliptic manifold, Oka manifold, Riemann surface, Arakelian's theorem, Mergelyan's theorem.

MSC: 30E10, 32E10, 32E30, 32H02

Language: English

DOI: 10.17323/1609-4514-2019-19-3-465-484