scholarly journals Localization of the Kobayashi metric and applications

2020 ◽  
Author(s):  
Jinsong Liu ◽  
Hongyu Wang
Keyword(s):  
Kobayashi Metric

The Lindelöf principle in ℂn

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Peter Dovbush
Keyword(s):  
Holomorphic Function ◽  
Bounded Domain ◽  
Lipschitz Condition ◽  
Function Theory ◽  
Riemann Sphere ◽  
Normal Function ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Kobayashi Metric ◽  
Lindelöf Principle

AbstractLet D be a bounded domain in ℂn. A holomorphic function f: D → ℂ is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ̅ℂ. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.

scholarly journals The Boundary Behavior of the Kobayashi Metric

1992 ◽  
Vol 22 (1) ◽  
pp. 227-234 ◽  
Author(s):  
Steven G. Krantz
Keyword(s):  
Boundary Behavior ◽  
Kobayashi Metric

Comparison of the Bergman and the Kobayashi metric

1980 ◽  
Vol 254 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Klas Diederich ◽  
John Erik Fornaess
Keyword(s):  
Kobayashi Metric

STATIONARY DISCS OF FIBRATIONS OVER THE CIRCLE

1995 ◽  
Vol 06 (06) ◽  
pp. 805-823 ◽  
Author(s):  
MIRAN ČERNE
Keyword(s):  
Unit Circle ◽  
Pseudoconvex Domains ◽  
Kobayashi Metric ◽  
Strictly Convex ◽  
Strongly Pseudoconvex Domains ◽  
Partial Indices ◽  
Stationary Disc ◽  
Polynomial Hull

Stationary discs of fibrations over the unit circle ∂D are considered. It is shown that if all fibers of a fibration Σ⊆∂D×Cn over the unit circle ∂D are strongly pseudoconvex hypersurfaces in Cn, then for every stationary disc f of the fibration Σ one can define the partial indices of f. In the case all fibers of Σ are strictly convex, it is proved that all partial indices of a stationary disc f are 0. It is also proved that in the case a stationary disc f of the fibration Σ is non-degenerate, the only possible partial indices of f are 0, 1 and –1. In particular, these results give information on the polynomial hull of Σ and new proofs of results related to the smoothness of the Kobayashi metric on some strongly pseudoconvex domains in Cn.

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
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