Klarreich, Erica Semiconjugacies between Kleinian group actions on the Riemann sphere. (English) Zbl 1011.30035 Am. J. Math. 121, No. 5, 1031-1078 (1999). The author discusses the action of a geometrically infinite Kleinian group \(\Gamma\) on the Riemann sphere and shows that in some conditions the semiconjugacy with the action of a geometrically finite Kleinian group is determined by the end invariants of \(\Gamma\). With respect to a semiconjugacy this discussion is related to the extension of a map of hyperbolic 3-space continuously to the boundary at infinity, that is the Riemann sphere. More generally, the author discusses the extension problem in the Gromov-hyperbolic spaces and gives a sufficient condition for a map between Gromov-hyperbolic spaces to be extend continuously to their boundaries. Reviewer: Gou Nakamura (Toyota) Cited in 1 ReviewCited in 48 Documents MSC: 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) Keywords:Kleinian group; semiconjugacy; Gromov-hyperbolic space; boundary at infinity; electric space PDFBibTeX XMLCite \textit{E. Klarreich}, Am. J. Math. 121, No. 5, 1031--1078 (1999; Zbl 1011.30035) Full Text: DOI Link