The Dynamics Theorem for CMC surfaces in R^3
| dc.creator | Meeks III, William H. | |
| dc.creator | Tinaglia, Giuseppe | |
| dc.date | 2008-05-09 | |
| dc.date.accessioned | 2026-07-07T09:38:12Z | |
| dc.date.available | 2026-07-07T09:38:12Z | |
| dc.description | In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in T(M), the set T(M') in T(M). Among various dynamics type results we prove that surfaces in minimal T-invariant sets of T(M) are chord-arc. We also show that if M has an infinite number of ends, then there exists a nonempty minimal T-invariant set in T(M) consisting entirely of surfaces with planes of Alexandrov symmetry. Finally, when M has a plane of Alexandrov symmetry, we prove the following characterization theorem: M has finite topology if and only if M has a finite number of ends greater than one. | |
| dc.description | 29 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0805.1427 | |
| dc.identifier | http://arxiv.org/abs/0805.1427 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160722 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10 | |
| dc.title | The Dynamics Theorem for CMC surfaces in R^3 | |
| dc.type | text |