Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities
In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we show that a semialgebraic CMC surface in $\mathbb{R}^3$ with isolated singular...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/844 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/844 |
| Access Level: | acceso abierto |
| Palabra clave: | CMC surfaces Classification Globally Subanalytic Sets |
| Sumario: | In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we show that a semialgebraic CMC surface in $\mathbb{R}^3$ with isolated singularities and suitable conditions on the singularities and of local connectedness is a plane or a finite union of round spheres and cylinders touching at the singularities. As a consequence, we obtain that a semialgebraic good CMC surface in $\mathbb{R}^3$ that is a topological manifold does not have isolated singularities and, moreover, it is a plane or a round sphere or a cylinder. A result in the case non-isolated singularities also is presented. |
|---|