dc.contributor.author Sampaio J. E. en_US dc.date.accessioned 2020-03-02T18:58:21Z dc.date.available 2020-03-02T18:58:21Z dc.date.issued 2020-03-02 dc.identifier.uri http://hdl.handle.net/20.500.11824/1093 dc.description.abstract In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic CMC surface in $\mathbb{R}^3$ with isolated singularities and a suitable condition of local connectedness is a plane or a finite union of round spheres and right circular cylinders touching at the singularities. en_US As a consequence, we obtain that a globally subanalytic CMC surface in $\mathbb{R}^3$ that is a topological manifold does not have isolated singularities. It is also proved that a connected closed globally subanalytic CMC surface in $\mathbb{R}^3$ with isolated singularities which is locally Lipschitz normally embedded needs to be a plane or a round sphere or a right circular cylinder. A result in the case of non-isolated singularities is also presented. It is also presented some results on regularity of semialgebraic sets and, in particular, it is proved a real version of Mumford's Theorem on regularity of normal complex analytic surfaces and a result about $C^1$ regularity of minimal varieties. dc.description.sponsorship The author was also partially supported by CNPq-Brazil grant 303811/2018-8 and Gobierno Vasco Grant IT1094-16. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Proceedings A of the Royal Society of Edinburgh en_US dc.relation info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation ES/1PE/SEV-2017-0718 en_US dc.relation EUS/BERC/BERC.2018-2021 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Classification of surfaces en_US dc.subject Constant mean curvature surfaces en_US dc.subject Semialgebraic Sets en_US dc.title Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/acceptedVersion en_US
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