A strong parametric h-principle for complete minimal surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913594733494272 |
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| author | Alarcon, Antonio Larusson, Finnur |
| author_facet | Alarcon, Antonio Larusson, Finnur |
| contents | We prove a parametric h-principle for complete nonflat conformal minimal immersions of an open Riemann surface $M$ into $\mathbb R^n$, $n\geq 3$. It follows that the inclusion of the space of such immersions into the space of all nonflat conformal minimal immersions is a weak homotopy equivalence. When $M$ is of finite topological type, the inclusion is a genuine homotopy equivalence. By a parametric h-principle due to Forstneric and Larusson, the space of complete nonflat conformal minimal immersions therefore has the same homotopy type as the space of continuous maps from $M$ to the punctured null quadric. Analogous results hold for holomorphic null curves $M\to\mathbb C^n$ and for full immersions in place of nonflat ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_03495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A strong parametric h-principle for complete minimal surfaces Alarcon, Antonio Larusson, Finnur Differential Geometry Complex Variables 53A10 (primary). 30F99, 32E30, 32H02, 32Q56, 54C55, 55M15 (secondary) We prove a parametric h-principle for complete nonflat conformal minimal immersions of an open Riemann surface $M$ into $\mathbb R^n$, $n\geq 3$. It follows that the inclusion of the space of such immersions into the space of all nonflat conformal minimal immersions is a weak homotopy equivalence. When $M$ is of finite topological type, the inclusion is a genuine homotopy equivalence. By a parametric h-principle due to Forstneric and Larusson, the space of complete nonflat conformal minimal immersions therefore has the same homotopy type as the space of continuous maps from $M$ to the punctured null quadric. Analogous results hold for holomorphic null curves $M\to\mathbb C^n$ and for full immersions in place of nonflat ones. |
| title | A strong parametric h-principle for complete minimal surfaces |
| topic | Differential Geometry Complex Variables 53A10 (primary). 30F99, 32E30, 32H02, 32Q56, 54C55, 55M15 (secondary) |
| url | https://arxiv.org/abs/2106.03495 |