From Stein manifolds to Oka manifolds: the h-principle in complex analysis
Abstract
This introduction to the homotopy principle in complex analysis and geometry, better known as the Oka theory, is aimed at wide mathematical audience. After a brief historical survey of the h-principle in smooth analysis and geometry, I present the key notions of Oka manifolds and Oka maps, which developed from the Oka-Grauert principle and Gromov's theory of elliptic complex manifolds and elliptic holomorphic submersions. I discuss recent and ongoing developments, open problems, and mention some applications. The paper also includes a brief survey of the recently developed h-principles in the classical theory of minimal surfaces.
Cite
@article{arxiv.2509.21197,
title = {From Stein manifolds to Oka manifolds: the h-principle in complex analysis},
author = {Franc Forstneric},
journal= {arXiv preprint arXiv:2509.21197},
year = {2025}
}
Comments
This is an invited contribution to Proceedings of the ICM 2026 in connection to author's invited lecture in Section Analysis