scholarly journals Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains

2000 ◽  
Vol 75 (3) ◽  
pp. 504-533 ◽  
Author(s):  
Z. M. Balogh ◽  
M. Bonk
Keyword(s):  
Gromov Hyperbolicity ◽  
Pseudoconvex Domains ◽  
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

Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains

1995 ◽  
Vol 38 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Siqi Fu
Keyword(s):  
Continuous Function ◽  
Asymptotic Expansions ◽  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Kobayashi Metric ◽  
Signed Distance ◽  
Strictly Pseudoconvex Domain ◽  
Kobayashi Metrics

AbstractIn this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that and|C(z,X)| ≤ C|X| for z ∊ U ∩ Ω and X ∊ ℂn

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