Minimal surfaces in Euclidean spaces by way of complex analysis
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917823576539136 |
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| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portorož on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of conformal minimal surfaces in Euclidean spaces. New results concern approximation, interpolation, and general position properties of minimal surfaces, existence of minimal surfaces with a given Gauss map, and the Calabi-Yau problem for minimal surfaces. To be accessible to a wide audience, the article includes a self-contained elementary introduction to the theory of minimal surfaces in Euclidean spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13347 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minimal surfaces in Euclidean spaces by way of complex analysis Forstneric, Franc Differential Geometry Primary 53A10, Secondary 32H02 This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portorož on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of conformal minimal surfaces in Euclidean spaces. New results concern approximation, interpolation, and general position properties of minimal surfaces, existence of minimal surfaces with a given Gauss map, and the Calabi-Yau problem for minimal surfaces. To be accessible to a wide audience, the article includes a self-contained elementary introduction to the theory of minimal surfaces in Euclidean spaces. |
| title | Minimal surfaces in Euclidean spaces by way of complex analysis |
| topic | Differential Geometry Primary 53A10, Secondary 32H02 |
| url | https://arxiv.org/abs/2108.13347 |