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arXiv · 2006.07888

Recent developments on Oka manifolds

Franc Forstneric
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Abstract

In this paper we present the main developments in Oka theory since the publication of my book Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis)}, Second Edition, Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for $n>1$ the fibre $\mathbb C^n$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.

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Franc Forstneric. 2020-06-14. Recent developments on Oka manifolds. https://doi.org/10.1016/j.indag.2023.01.005

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