Horosphere topology

• Filippo Bracci ^[2] ; Hervé Gaussier ^[1]
  1. [1] Grenoble Alpes University

     Grenoble Alpes University

     Arrondissement de Grenoble, Francia

     
  2. [2] Università di Roma Tor Vergata, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 20, Nº 1, 2020, págs. 239-289
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We introduce a prime end-type theory on complete Kobayashi hyperbolic manifolds using horosphere sequences. This allows to introduce a new notion of boundary – new even in the unit disc in the complex space – the horosphere boundary, and a topology on the manifold together with its horosphere boundary, the horosphere topology. We prove that a bounded strongly pseudoconvex domain endowed with the horosphere topology is homeomorphic to its Euclidean closure, while for the polydisc such a horosphere topology is not even Hausdorff and is different from the Gromov topology. We use this theory to study boundary behavior of univalent maps from bounded strongly pseudoconvex domains.