The Differential of a Quasi-Conformal Mapping of a Carnot-Caratheodory Space View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1995

AUTHORS

G. A. Margulis , G. D. Mostow

ABSTRACT

The theory of quasi-conformal mappings has been used to prove rigidity theorems on hyperbolic n space over the division algebras ℝ, ℂ, ℍ, and \({\Bbb O}\), by studying quasi-conformal mappings on their boundary spheres S kn−1 at infinity, where k is the dimension of the division algebra. The notion of quasiconformal mappings for such spaces, first introduced in [Mo2]w, as subsequently reformulated by Pansu in terms of Carnot-Caratheodory spaces M, and Pansu studied quasi-conformal mappings for the special case of graded nilpotent groups M. Subsequently, Pansu’s definition was simplified in [Mo3], and this simpler definition was employed by Koranyi-Reimann in their study of quasi-conformal mappings of the nilpotent Heisenberg group operating on the boundary of complex hyperbolic n-space and transitive on the complement of one point. More... »

PAGES

402-433

Book

TITLE

Geometries in Interaction

ISBN

978-3-0348-9907-9
978-3-0348-9102-8

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-9102-8_10

DOI

http://dx.doi.org/10.1007/978-3-0348-9102-8_10

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035936281


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