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Article: Fridman function, injectivity radius function and squeezing function

TitleFridman function, injectivity radius function and squeezing function
Authors
KeywordsFridman function
Injectivity radius
Squeezing function
Invariant metrics
Issue Date2021
PublisherSpringer.
Citation
The Journal of Geometric Analysis, 2021, v. 32 How to Cite?
AbstractVery recently, the Fridman function of a complex manifold X has been identified as a dual of the squeezing function of X. In this paper, we prove that the Fridman function for certain hyperbolic complex manifold X is bounded above by the injectivity radius function of X. This result also suggests us to use the Fridman function to extend the definition of uniform thickness to higher dimensional hyperbolic complex manifolds. We also establish an expression for the Fridman function (with respect to the Kobayashi metric) when X = D/Γ and Γ is a torsion-free discrete subgroup of isometries on the standard open unit disk D. Hence explicit formulae of the Fridman functions for the annulus A_r and the punctured disk D∗ are derived. These are the first explicit non-constant Fridman functions. Finally, we explore the boundary behavior of the Fridman functions (with respect to the Kobayashi metric) and the squeezing functions for regular type hyperbolic Riemann surfaces and planar domains, respectively.
Persistent Identifierhttp://hdl.handle.net/10722/312675
ISSN
2023 Impact Factor: 1.2
2023 SCImago Journal Rankings: 1.203
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorNg, TW-
dc.contributor.authorTANG, CC-
dc.contributor.authorTsai, HTJ-
dc.date.accessioned2022-05-12T10:54:03Z-
dc.date.available2022-05-12T10:54:03Z-
dc.date.issued2021-
dc.identifier.citationThe Journal of Geometric Analysis, 2021, v. 32-
dc.identifier.issn1050-6926-
dc.identifier.urihttp://hdl.handle.net/10722/312675-
dc.description.abstractVery recently, the Fridman function of a complex manifold X has been identified as a dual of the squeezing function of X. In this paper, we prove that the Fridman function for certain hyperbolic complex manifold X is bounded above by the injectivity radius function of X. This result also suggests us to use the Fridman function to extend the definition of uniform thickness to higher dimensional hyperbolic complex manifolds. We also establish an expression for the Fridman function (with respect to the Kobayashi metric) when X = D/Γ and Γ is a torsion-free discrete subgroup of isometries on the standard open unit disk D. Hence explicit formulae of the Fridman functions for the annulus A_r and the punctured disk D∗ are derived. These are the first explicit non-constant Fridman functions. Finally, we explore the boundary behavior of the Fridman functions (with respect to the Kobayashi metric) and the squeezing functions for regular type hyperbolic Riemann surfaces and planar domains, respectively.-
dc.languageeng-
dc.publisherSpringer.-
dc.relation.ispartofThe Journal of Geometric Analysis-
dc.rightsThis version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/[insert DOI]-
dc.subjectFridman function-
dc.subjectInjectivity radius-
dc.subjectSqueezing function-
dc.subjectInvariant metrics-
dc.titleFridman function, injectivity radius function and squeezing function-
dc.typeArticle-
dc.identifier.emailNg, TW: ngtw@hku.hk-
dc.identifier.authorityNg, TW=rp00768-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1007/s12220-021-00818-7-
dc.identifier.hkuros332998-
dc.identifier.volume32-
dc.identifier.isiWOS:000728589600001-
dc.publisher.placeSwitzerland-

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