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dc.contributor.authorHe, Chan-
dc.contributor.authorMartini, Horst-
dc.contributor.authorWu, Senlin-
dc.date.accessioned2020-02-12T13:05:54Z-
dc.date.available2020-02-12T13:05:54Z-
dc.date.issued2013-
dc.identifier.urihttp://hdl.handle.net/10662/10317-
dc.description.abstractIt is well known that the construction of Voronoi diagrams is based on the notion of bisector of two given points. Already in normed linear spaces, bisectors have a complicated structure and can, for many classes of norms, only be described with the help of topological methods. Even more general, we present results on bisectors for convex distance functions (gauges). Let C, with the origin o from its interior, be the compact, convex set inducing a convex distance function (gauge) in the plane, and let B( ̶ x, x) be the bisector of ̶ x and x, i.e., the set of points z whose distance (measured with the convex distance function induced by C) to ̶ x equals that to x. For example, we prove the following characterization of the Euclidean norm within the family of all convex distance functions: if the set L of points x in the boundary ∂C of C that create B( ̶ x, x) as a straight line has non-empty interior with respect to ∂C, then C is an ellipse centered at the origin. For the subcase of normed planes we give an easier approach, extending the result also to higher dimensions.es_ES
dc.format.extent20 p.es_ES
dc.format.mimetypeapplication/pdfen_US
dc.language.isoenges_ES
dc.publisherUniversidad de Extremaduraes_ES
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectBirkhoff orthogonalityes_ES
dc.subjectBisectores_ES
dc.subjectCharacterization of ellipsees_ES
dc.subjectConvex distance functiones_ES
dc.subjectEuclidean normes_ES
dc.subjectGaugees_ES
dc.subjectIsosceles orthogonalityes_ES
dc.subjectRoberts orthogonalityes_ES
dc.subjectVoronoi diagrames_ES
dc.subjectOrtogonalidad de Birkhoffes_ES
dc.subjectBisectrizes_ES
dc.subjectCaracterización de elipsees_ES
dc.subjectFunción de distancia convexaes_ES
dc.subjectNorma euclidianaes_ES
dc.subjectIndicadores_ES
dc.subjectOrtogonalidad isósceleses_ES
dc.subjectOrtogonalidad de Robertses_ES
dc.subjectDiagrama de Voronoies_ES
dc.titleOn bisectors for convex distance functionses_ES
dc.typearticlees_ES
dc.description.versionpeerReviewedes_ES
europeana.typeTEXTen_US
dc.rights.accessRightsopenAccesses_ES
dc.subject.unesco1202 Análisis y Análisis Funcionales_ES
dc.subject.unesco1204.06 Geometría Euclídeaes_ES
europeana.dataProviderUniversidad de Extremadura. Españaes_ES
dc.identifier.bibliographicCitationHE, CH., MARTINI, H., WU,S. (2013). On bisectors for convex distance functions. Extracta Mathematicae 28 (1), 57-76. E-ISSN 2605-5686es_ES
dc.type.versionpublishedVersiones_ES
dc.contributor.affiliationHarbin University of Science and Technology. Chinaen_US
dc.contributor.affiliationChemnitz University of Technology. Germanyen_US
dc.identifier.publicationtitleExtracta Mathematicaees_ES
dc.identifier.publicationissue1es_ES
dc.identifier.publicationfirstpage57es_ES
dc.identifier.publicationlastpage76es_ES
dc.identifier.publicationvolume28es_ES
dc.identifier.e-issn2605-5686-
Colección:Extracta Mathematicae Vol. 28, nº 1 (2013)

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