an:01356008
Zbl 1011.30035
Klarreich, Erica
Semiconjugacies between Kleinian group actions on the Riemann sphere
EN
Am. J. Math. 121, No. 5, 1031-1078 (1999).
00059684
1999
j
30F40
Kleinian group; semiconjugacy; Gromov-hyperbolic space; boundary at infinity; electric space
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.
Gou Nakamura (Toyota)