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dc.contributor.authorSampaio J. E.en_US
dc.description.abstractIn 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. 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.en_US
dc.description.sponsorshipThe author was also partially supported by CNPq-Brazil grant 303811/2018-8 and Gobierno Vasco Grant IT1094-16.en_US
dc.publisherProceedings A of the Royal Society of Edinburghen_US
dc.subjectClassification of surfacesen_US
dc.subjectConstant mean curvature surfacesen_US
dc.subjectSemialgebraic Setsen_US
dc.titleGlobally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularitiesen_US

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