Show simple item record

dc.contributor.authorSampaio J. E.en_US
dc.date.accessioned2020-03-02T18:58:21Z
dc.date.available2020-03-02T18:58:21Z
dc.date.issued2020-03-02
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1093
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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherProceedings A of the Royal Society of Edinburghen_US
dc.relationinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.relationES/1PE/SEV-2017-0718en_US
dc.relationEUS/BERC/BERC.2018-2021en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_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
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

info:eu-repo/semantics/openAccess
Except where otherwise noted, this item's license is described as info:eu-repo/semantics/openAccess