The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913568126926848 |
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| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | In this paper, we show that if $(X,g)$ is an oriented four dimensional Einstein manifold which is self-dual or anti-self-dual then superminimal surfaces in $X$ of appropriate spin enjoy the Calabi-Yau property, meaning that every immersed surface of this type from a bordered Riemann surface can be uniformly approximated by complete superminimal surfaces with Jordan boundaries. The proof uses the theory of twistor spaces and the Calabi-Yau property of holomorphic Legendrian curves in complex contact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_03536 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds Forstneric, Franc Differential Geometry Complex Variables Primary 53A10, 53C25, 53C26. Secondary 32E30, 37J55 In this paper, we show that if $(X,g)$ is an oriented four dimensional Einstein manifold which is self-dual or anti-self-dual then superminimal surfaces in $X$ of appropriate spin enjoy the Calabi-Yau property, meaning that every immersed surface of this type from a bordered Riemann surface can be uniformly approximated by complete superminimal surfaces with Jordan boundaries. The proof uses the theory of twistor spaces and the Calabi-Yau property of holomorphic Legendrian curves in complex contact manifolds. |
| title | The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds |
| topic | Differential Geometry Complex Variables Primary 53A10, 53C25, 53C26. Secondary 32E30, 37J55 |
| url | https://arxiv.org/abs/2004.03536 |