Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 321-329
Syracuse University, Department of Mathematics
Syracuse, NY 13244, U.S.A.; lvkovale 'at' syr.edu
Syracuse University, Department of Mathematics
Syracuse, NY 13244, U.S.A.; jkonnine 'at' syr.edu
Abstract. We extend delta-monotone quasiconformal mappings from dimension n to n + 1 while preserving both monotonicity and quasiconformality. This gives an analytic proof of the extendability of quasiconformal mappings that can be factored into bi-Lipschitz and delta-monotone mappings. In the case n = 1 our approach yields a refinement of the Beurling-Ahlfors extension.
2000 Mathematics Subject Classification: Primary 30C65; Secondary 47H05, 47B34.
Key words: Quasiconformal mapping, extension, monotone mapping.
Reference to this article: L.V. Kovalev and J. Onninen: An N-dimensional version of the Beurling-Ahlfors extension. Ann. Acad. Sci. Fenn. Math. 36 (2011), 321-329.
doi:10.5186/aasfm.2011.3620
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