Estimates of the Kobayashi and quasi-hyperbolic distances

Nikolov, Nikolai; Andreev, Lyubomir

doi:10.1007/s10231-016-0561-z

Cited by 26 publications

(20 citation statements)

References 8 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If ∂D is Dini-smooth, then D has 1 2 -log-growth by [NA,Corollary 8]. However, there exist C 1 -smooth (but not Dini-smooth) domains for which D has not 1 2 -log-growth [NPT,Example 2].…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Visibility of Kobayashi geodesics in convex domains and related properties

Bracci¹,

Nikolov²,

Thomas³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Let D ⊂ C n be a bounded convex domain. A pair of distinct boundary points {p, q} of D has the visibility property provided there exist a compact subset K p,q ⊂ D and open neighborhoods U p of p and U q of q, such that the real geodesics for the Kobayashi metric of D which join points in U p and U q intersect K p,q . Every Gromov hyperbolic convex domain enjoys the visibility property for any couple of boundary points. The Goldilocks domains introduced by Bharali and Zimmer and the log-type domains of Liu and Wang also enjoys the visibility property.In this paper we prove that a certain estimate on the growth of the Kobayashi distance near the boundary points is a necessary condition for visibility and provide new cases where this estimate and the visibility property hold.We also exploit visibility for studying the boundary behavior of biholomorphic maps.

show abstract

“…If ∂D is Dini-smooth, then D has 1 2 -log-growth by [NA,Corollary 8]. However, there exist C 1 -smooth (but not Dini-smooth) domains for which D has not 1 2 -log-growth [NPT,Example 2].…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

“…Proof of Theorem 1.2. By [NA,Corollary 8] the domain D has 1 2 -log-growth. Since F p = {p} for any p ∈ ∂D by the hypothesis, Theorem 4.1 shows that any pair of distinct points {p, q} in ∂D verifies the standard estimate.…”

Section: Visibility and Growth Of The Metricmentioning

confidence: 99%