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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)", 2nd ed., 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.
Keywords: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property
Published in DiRROS: 14.03.2024; Views: 418; Downloads: 454
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