Constructing solutions to the Björling problem for isothermic surfaces by structure preserving discretization

dc.contributor.authorBücking, Ulrike
dc.contributor.authorMatthes, Daniel
dc.date.accessioned2017-09-01T08:04:39Z
dc.date.available2017-09-01T08:04:39Z
dc.date.issued2016
dc.description.abstractIn this article, we study an analog of the Björling problem for isothermic surfaces (that are a generalization of minimal surfaces): given a regular curve γ in R3 and a unit normal vector field n along γ, find an isothermic surface that contains γ, is normal to n there, and is such that the tangent vector γ′ bisects the principal directions of curvature. First, we prove that this problem is uniquely solvable locally around each point of γ, provided that γ and n are real analytic. The main result is that the solution can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is read off from γ, and then passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.en
dc.identifier.isbn978-3-662-50447-5
dc.identifier.urihttp://depositonce.tu-berlin.de/handle/11303/6689
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-6130
dc.language.isoen
dc.relation.ispartof10.1007/978-3-662-50447-5
dc.rights.urihttps://creativecommons.org/licenses/by-nc/2.5/
dc.subject.ddc510 Mathematik
dc.titleConstructing solutions to the Björling problem for isothermic surfaces by structure preserving discretizationen
dc.typeBook Part
dc.type.versionpublishedVersion
dcterms.bibliographicCitation.booktitleAdvances in discrete differential geometry
dcterms.bibliographicCitation.doi10.1007/978-3-662-50447-5_10
dcterms.bibliographicCitation.editorBobenko, Alexander I.
dcterms.bibliographicCitation.originalpublishernameSpringer
dcterms.bibliographicCitation.originalpublisherplaceBerlin, Heidelberg
dcterms.bibliographicCitation.pageend345
dcterms.bibliographicCitation.pagestart309
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlin
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