Helicoidal minimal surfaces of prescribed genus, I
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2013
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910306909814784 |
|---|---|
| author | Hoffman, David Traizet, Martin White, Brian |
| author_facet | Hoffman, David Traizet, Martin White, Brian |
| contents | For every genus g, we prove that S^2 x R contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the S^2 tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in Euclidean 3-space R^3 that are helicoidal at infinity. In a companion paper, we prove that helicoidal surfaces in R^3 of every prescribed genus occur as such limits of examples in S^2 x R. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_5861 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Helicoidal minimal surfaces of prescribed genus, I Hoffman, David Traizet, Martin White, Brian Differential Geometry 53A10 (primary) 49Q05, 53C42 (secondary) For every genus g, we prove that S^2 x R contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the S^2 tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in Euclidean 3-space R^3 that are helicoidal at infinity. In a companion paper, we prove that helicoidal surfaces in R^3 of every prescribed genus occur as such limits of examples in S^2 x R. |
| title | Helicoidal minimal surfaces of prescribed genus, I |
| topic | Differential Geometry 53A10 (primary) 49Q05, 53C42 (secondary) |
| url | https://arxiv.org/abs/1304.5861 |