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Algebraic CMC hypersurfaces of order 3 in Euclidean spaces
Department of Mathematics, Central Connecticut State University, New Britain, USA.ORCID iD: 0000-0002-9647-2875
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
2019 (English)In: Journal of Geometry, ISSN 0047-2468, E-ISSN 1420-8997, Vol. 110, no 1, article id 110:6Article in journal (Refereed) Published
Abstract [en]

Understanding and finding of general algebraic constant mean curvature surfaces in the Euclidean spaces is a hard open problem. The basic examples are the standard spheres and the round cylinders, all defined by a polynomial of degree 2. In this paper, we prove that thereare no algebraic hypersurfaces of degree 3 in higherdimensional (n>2) Euclidean spaces, with nonzero constant mean curvature.

Place, publisher, year, edition, pages
Basel, Switzerland: Birkhaeuser Science , 2019. Vol. 110, no 1, article id 110:6
Keywords [en]
Constant mean curvature; algebraic surfaces
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-153452DOI: 10.1007/s00022-018-0461-zScopus ID: 2-s2.0-85058816832OAI: oai:DiVA.org:liu-153452DiVA, id: diva2:1271707
Available from: 2018-12-18 Created: 2018-12-18 Last updated: 2019-01-08Bibliographically approved

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Tkachev, Vladimir G.

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