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Prime ends theory in higher dimension Gaussier, Herve


This is a joint work with Filippo Bracci. We try to extend the Carath\'eodory prime ends theory in higher dimension, defining the "horosphere boundary" of complete hyperbolic (in the sense of Kobayashi) manifolds. We prove that a strongly pseudoconvex domain together with its horosphere boundary, endowed with the horosphere topology, is homeomorphic to its Euclidean closure, whereas the horosphere boundary of a polydisc is not even Hausdorff. As an application we study the boundary behaviour of univalent mappings.

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