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...
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2018 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositório: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/844 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/844 |
| Access Level: | Acceso aberto |
| Palavra-chave: | CMC surfaces Classification Globally Subanalytic Sets |
| Resumo: | 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. |
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