Unbounded visibility domains, the end compactification, and applications
نویسندگان
چکیده
In this paper we study when the Kobayashi distance on a hyperbolic domain has certain visibility properties, with focus unbounded domains. “Visibility” in context is reminiscent of visibility, seen negatively curved Riemannian manifolds, sense Eberlein–O’Neill. However, do not assume that domains studied are Cauchy-complete respect to distance, as hard establish for C d \mathbb {C}^d , alttext="d greater-than-or-equal-to 2"> ? 2 encoding="application/x-tex">d \geq 2 . We various ways which property controls boundary behavior holomorphic maps. Among these results Carathéodory-type extension theorem biholomorphisms between planar domains—notably: infinitely-connected also explore connections our and Gromov hyperbolicity distance.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2023
ISSN: ['2330-0000']
DOI: https://doi.org/10.1090/tran/8944