kobayashi distance
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2018 ◽  
Vol 30 (1) ◽  
pp. 159-170
Author(s):  
Peter Pflug ◽  
Włodzimierz Zwonek

Abstract We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains. The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry of non-Gromov hyperbolic convex domains. A connection between the Hilbert metric of a convex domain Ω in {\mathbb{R}^{n}} with the Kobayashi distance of the tube domain over the domain Ω is also shown. Moreover, continuity properties up to the boundary of complex geodesics in tube domains with a smooth convex bounded base are also studied in detail.


2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Nikolai Nikolov ◽  
Pascal J. Thomas ◽  
Maria Trybuła
Keyword(s):  

AbstractWe prove the Gromov non-hyperbolicity with respect to the Kobayashi distance for


2015 ◽  
Vol 19 (2) ◽  
pp. 535-552 ◽  
Author(s):  
Monika Budzyńska ◽  
Tadeusz Kuczumow ◽  
Simeon Reich

2014 ◽  
Vol 362 (1-2) ◽  
pp. 425-449 ◽  
Author(s):  
Giorgio Patrizio ◽  
Andrea Spiro

2010 ◽  
Vol 89 (3) ◽  
pp. 297-307 ◽  
Author(s):  
MONIKA BUDZYŃSKA ◽  
SIMEON REICH

AbstractUsing the Kobayashi distance, we provide sufficient conditions for the intersection of a family of holomorphic retracts in a Banach space to also be a holomorphic retract.


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