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Quasiconformal groups and the conical limit set. (English) Zbl 0654.30013
Holomorphic functions and moduli II, Proc. Workshop, Berkeley/Calif. 1986, Publ., Math. Sci. Res. Inst. 11, 59-67 (1988).
[For the entire collection see Zbl 0646.00005.]
Let G be a discrete quasiconformal group acting on the unit ball B in R n where \(n\geq 2\). The authors study the conical limit set \(L_ c(G)\subset \partial B\) of G and prove three theorems about the (n-1)-dimensional measure of \(L_ c(G)\). Earlier related results include works of Sullivan and Tukia. The main ingredients in the proofs are well-known distortion properties of Möbius transformations and quasiconformal mappings together with Gehring’s L p-integrability theorem for the partial derivatives of quasiconformal mappings.
Reviewer: M.Vuorinen

MSC:
30C62 Quasiconformal mappings in the complex plane