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dc.contributor.authorSkopenkov, Mikhail
dc.contributor.authorPottmann, Helmut
dc.contributor.authorGrohs, Philipp
dc.date.accessioned2015-08-03T09:33:43Z
dc.date.available2015-08-03T09:33:43Z
dc.date.issued2011-10-30
dc.identifier.issn00255874
dc.identifier.doi10.1007/s00209-011-0953-0
dc.identifier.urihttp://hdl.handle.net/10754/561903
dc.description.abstractA Laguerre minimal surface is an immersed surface in ℝ 3 being an extremal of the functional ∫ (H 2/K-1)dA. In the present paper, we prove that the only ruled Laguerre minimal surfaces are up to isometry the surfaces ℝ (φλ) = (Aφ, Bφ, Cφ + D cos 2φ) + λ(sin φ, cos φ, 0), where A,B,C,D ε ℝ are fixed. To achieve invariance under Laguerre transformations, we also derive all Laguerre minimal surfaces that are enveloped by a family of cones. The methodology is based on the isotropic model of Laguerre geometry. In this model a Laguerre minimal surface enveloped by a family of cones corresponds to a graph of a biharmonic function carrying a family of isotropic circles. We classify such functions by showing that the top view of the family of circles is a pencil. © 2011 Springer-Verlag.
dc.description.sponsorshipThe authors are grateful to S. Ivanov for useful discussions. M. Skopenkov was supported in part by Mobius Contest Foundation for Young Scientists and the Euler Foundation. H. Pottmann and P. Grohs are partly supported by the Austrian Science Fund (FWF) under grant S92.
dc.publisherSpringer Nature
dc.subjectBiharmonic function
dc.subjectLaguerre geometry
dc.subjectLaguerre minimal surface
dc.subjectRuled surface
dc.titleRuled Laguerre minimal surfaces
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.identifier.journalMathematische Zeitschrift
dc.contributor.institutionInstitute for Information Transmission Problems of the Russian Academy of Sciences, Bolshoy Karetny per. 19, bld. 1, Moscow 127994, Russian Federation
dc.contributor.institutionSeminar for Applied Mathematics, ETH Zentrum, Rämistrasse 101, 8092 Zurich, Switzerland
dc.identifier.arxividarXiv:1011.0272
kaust.personSkopenkov, Mikhail
kaust.personPottmann, Helmut
dc.date.published-online2011-10-30
dc.date.published-print2012-10


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