Gromov hyperbolicity of the Kobayashi metric on C-convex domains

2018 ◽  
Vol 468 (2) ◽  
pp. 1164-1178 ◽  
Author(s):  
Nikolai Nikolov ◽  
Maria Trybuła
Keyword(s):  
Gromov Hyperbolicity ◽  
Kobayashi Metric ◽  
Convex Domains

scholarly journals Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains

2018 ◽  
Vol 30 (1) ◽  
pp. 159-170
Author(s):  
Peter Pflug ◽  
Włodzimierz Zwonek
Keyword(s):  
Convex Domain ◽  
Gromov Hyperbolicity ◽  
Smooth Convex ◽  
Tube Domain ◽  
Convex Domains ◽  
Hilbert Metric ◽  
Kobayashi Distance ◽  
Continuity Properties ◽  
Gromov Hyperbolic ◽  
Tube Domains

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.

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