Identificador persistente para citar o vincular este elemento: http://hdl.handle.net/10662/10317
Títulos: On bisectors for convex distance functions
Autores/as: He, Chan
Martini, Horst
Wu, Senlin
Palabras clave: Birkhoff orthogonality;Bisector;Characterization of ellipse;Convex distance function;Euclidean norm;Gauge;Isosceles orthogonality;Roberts orthogonality;Voronoi diagram;Ortogonalidad de Birkhoff;Bisectriz;Caracterización de elipse;Función de distancia convexa;Norma euclidiana;Indicador;Ortogonalidad isósceles;Ortogonalidad de Roberts;Diagrama de Voronoi
Fecha de publicación: 2013
Editor/a: Universidad de Extremadura
Resumen: It 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.
URI: http://hdl.handle.net/10662/10317
Colección:Extracta Mathematicae Vol. 28, nº 1 (2013)

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