Mergelyan's and Arakelian's theorems for manifold-valued maps
Complex Variables
2020-04-16 v3
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 the plane to any compact complex homogeneous manifold.
Keywords
Cite
@article{arxiv.1801.04773,
title = {Mergelyan's and Arakelian's theorems for manifold-valued maps},
author = {Franc Forstneric},
journal= {arXiv preprint arXiv:1801.04773},
year = {2020}
}
Comments
The exposition has been improved and a new Section 5 has been added. To appear in J. Moscow Math. Soc