Geometry of Metrics

Abstract

During the past thirty years hyperbolic type metrics have become popular tools also in modern mapping theory, e.g., in the study of quasiconformal and quasiregular maps in the euclidean $n$-space. We study here several metrics that one way or another are related to modern mapping theory and point out many open problems dealing with the geometry of such metrics.

This informal paper is based on the author's lectures in Chennai, India, in the ICM2010 Satellite Conference International Workshop on Harmonic and Quasiconformal Mappings (HQM2010) in August 2010

References in corpus (3)

• Local Convexity Properties of Quasihyperbolic Balls in Punctured Space
• Moduli of Continuity of Quasiregular Mappings
• Inequalities and geometry of hyperbolic-type metrics, radius problems and norm estimates