Annales Academię Scientiarum Fennicę
Mathematica
Volumen 35, 2010, 221-233
California State University, Department of Mathematics
Fullerton, CA 92834, U.S.A.; zibragimov 'at' fullerton.edu
Abstract. We show that it is possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the real line to a quasi-isometry of the upper-half plane. Epstein and Markovic have recently shown that a homomorphic extension to quasiconformal homeomorphisms of the upper-half plane is not possible.
2000 Mathematics Subject Classification: Primary 30C62, 37E10, 37E30.
Key words: Quasiconformal mappings, quasisymmetric mappings, quasi-isometry, convergence groups, hyperbolic space.
Reference to this article: Z. Ibragimov: Quasi-isometric extensions of quasisymmetric mappings of the real line compatible with composition. Ann. Acad. Sci. Fenn. Math. 35 (2010), 221-233.
doi:10.5186/aasfm.2010.3513
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