Carleman approximation by non-critical functions on Riemann surfaces
Complex Variables
2025-12-18 v2
Abstract
We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous functions can be approximated by non-critical holomorphic ones. We also consider a different approach, which in some cases gives uniform approximation by non-critical holomorphic functions on more general sets than semi-admissible ones.
Cite
@article{arxiv.2508.05765,
title = {Carleman approximation by non-critical functions on Riemann surfaces},
author = {Beno Učakar},
journal= {arXiv preprint arXiv:2508.05765},
year = {2025}
}
Comments
13 pages, 2 figures. Title changed. Minor revisions to address typos and improve the exposition. To appear in the journal Analysis and Mathematical Physics