Notions of Visibility with respect to the Kobayashi distance: Comparison and Applications

Chandel, Vikramjeet Singh; Maitra, Anwoy; Sarkar, Amar Deep

doi:10.48550/arxiv.2111.00549

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, visibility (with respect to the Euclidan boundary) has been exhibited for domains which are not Gromov hyperbolic in [3,2,10,17], and turns out to be a key notion for continuous extension of biholomorphisms and Denjoy-Wolff type theorems. In [13], this notion has been extended to embedded submanifolds of C d .…”

Section: Introductionmentioning

confidence: 99%

Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance

Bracci¹,

Gaussier²,

Nikolov³

et al. 2022

Preprint

View full text Add to dashboard Cite

We introduce the notion of locally visible and locally Gromov hyperbolic domains in C d . We prove that a bounded domain in C d is locally visible and locally Gromov hyperbolic if and only if it is (globally) visible and Gromov hyperbolic with respect to the Kobayashi distance. This allows to construct new classes of domains which are Gromov hyperbolic and for which biholomorphisms extend continuously up to the boundary.

show abstract