An end-to-end construction of doubly periodic minimal surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2016
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912398379581440 |
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| author | Connor, Peter Li, Kevin |
| author_facet | Connor, Peter Li, Kevin |
| contents | Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations. The genus 2n-1 family converges smoothly to 2n copies of Scherk's doubly periodic minimal surface. The only previously known doubly periodic minimal surfaces with parallel ends and genus greater than 3 limit in a foliation of Euclidean space by parallel planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_06440 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | An end-to-end construction of doubly periodic minimal surfaces Connor, Peter Li, Kevin Differential Geometry 53A10, 49Q05, 53C42 Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations. The genus 2n-1 family converges smoothly to 2n copies of Scherk's doubly periodic minimal surface. The only previously known doubly periodic minimal surfaces with parallel ends and genus greater than 3 limit in a foliation of Euclidean space by parallel planes. |
| title | An end-to-end construction of doubly periodic minimal surfaces |
| topic | Differential Geometry 53A10, 49Q05, 53C42 |
| url | https://arxiv.org/abs/1604.06440 |