From Stein manifolds to Oka manifolds: the h-principle in complex analysis
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911176201338880 |
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| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Stein manifolds to Oka manifolds: the h-principle in complex analysis Forstneric, Franc Complex Variables Differential Geometry Primary 32Q56. Secondary 32H02, 14R10, 53D35 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. |
| title | From Stein manifolds to Oka manifolds: the h-principle in complex analysis |
| topic | Complex Variables Differential Geometry Primary 32Q56. Secondary 32H02, 14R10, 53D35 |
| url | https://arxiv.org/abs/2509.21197 |