Barrlund's distance function and quasiconformal maps
Masayo Fujimura, Marcelina Mocanu, Матти Вуоринен
Abstract
Answering a question about triangle inequality suggested by R. Li, Barrlund [The p-relative distance is a metric. SIAM J Matrix Anal Appl. 1999;21:699.702] introduced a distance function which is a metric on a subdomain of Rn. We study this Barrlund metric and give sharp bounds for it in terms of other metrics of current interest. We also prove sharp distortion results for the Barrlund metric under quasiconformal maps.
Topics & Concepts
MathematicsMetric (unit)Function (biology)Distortion (music)Triangle inequalityEquivalence of metricsMathematical analysisMatrix (chemical analysis)Pure mathematicsCombinatoricsMetric spaceProduct metricOperations managementElectronic engineeringAmplifierEconomicsBiologyCMOSComposite materialEngineeringMaterials scienceEvolutionary biologyAnalytic and geometric function theoryNonlinear Partial Differential EquationsGeometric Analysis and Curvature Flows