# Moscow Mathematical Journal

Volume 19, Issue 3, July–September 2019  pp. 465–484.

Mergelyan's and Arakelian's Theorems for Manifold-Valued Maps

Authors:  F. Forstnerič (1)
Author institution:(1) Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia,
Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

Summary:

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.

2010 Math. Subj. Class. 30E10, 32E10, 32E30, 32H02.

Keywords: Holomorphic map, homogeneous manifold, elliptic manifold, Oka manifold, Riemann surface, Arakelian's theorem, Mergelyan's theorem.