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Quasihyperbolic Geometry in Euclidean and Banach Spaces

By Riku Klén, Antti Rasila and Jarno Talponen

Abstract

We consider the quasihyperbolic metric, and its generalizations in both the $n$-dimensional Euclidean space $R^n$, and in Banach spaces. Historical background, applications, and our recent work on convexity properties of these metrics are discussed.Comment: ICM 2010 - Satellite Conference International Workshop on Harmonic and Quasiconformal Mappings (HQM2010), IIT Madras, August 09-17, 2010. 18 pages, 5 figure

Topics: Mathematics - Complex Variables, Mathematics - Functional Analysis, Primary 30C65, Secondary 46T05
Year: 2011
OAI identifier: oai:arXiv.org:1104.3745
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