Abstract
We study the complex geometry of a class of domains in C n which generalize the annuli in C, i.e., which are quotients of the unit ball B n of C n for the action of a group gen- erated by a hyperbolic element of AutB n . In particular, we prove that the degree of holomor- phic maps between two such domains is bounded by a constant which depends on the ''radii'' of the domains only and we give some results on the existence of complex geodesics for the Kobayashi distance in these domains.
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