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On necessary and sufficient conditions for the Kobayashi hyperbolicity of tube domains in C²

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Isaev, Alexander

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This note concerns tube domains in C² with the envelope of holomorphy not equal to the entire space. We construct examples showing that for such domains the sufficient condition for Kobayashi hyperbolicity due to M. Jarnicki and P. Pflug cannot be replaced by its weaker “affine” variant, which is known to be a necessary condition for hyperbolicity. Thus, we arrive at the somewhat unexpected conclusion that the obstructions for a domain in the above class to be Kobayashi hyperbolic are not just...[Show more]

dc.contributor.authorIsaev, Alexander
dc.date.accessioned2018-01-04T00:57:20Z
dc.identifier.issn0022-247X
dc.identifier.urihttp://hdl.handle.net/1885/139055
dc.description.abstractThis note concerns tube domains in C² with the envelope of holomorphy not equal to the entire space. We construct examples showing that for such domains the sufficient condition for Kobayashi hyperbolicity due to M. Jarnicki and P. Pflug cannot be replaced by its weaker “affine” variant, which is known to be a necessary condition for hyperbolicity. Thus, we arrive at the somewhat unexpected conclusion that the obstructions for a domain in the above class to be Kobayashi hyperbolic are not just “affine”.
dc.format.mimetypeapplication/pdf
dc.publisherElsevier
dc.rights© 2017 Elsevier B.V.
dc.sourceJournal of Mathematical Analysis and Applications
dc.subjectKobayashi hyperbolicity
dc.subjectTube domains in complex space
dc.titleOn necessary and sufficient conditions for the Kobayashi hyperbolicity of tube domains in C²
dc.typeJournal article
local.identifier.citationvolume460
dc.date.issued2018-04-01
local.identifier.ariespublicationa383154xPUB8836
local.publisher.urlhttps://www.elsevier.com/
local.type.statusAccepted Version
local.contributor.affiliationIsaev, A., Department of Mathematics, Mathematical Sciences Institute, The Australian National University
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage58
local.bibliographicCitation.lastpage62
local.identifier.doi10.1016/j.jmaa.2017.11.043
dcterms.accessRightsOpen Access
dc.provenancehttp://www.sherpa.ac.uk/romeo/issn/0022-247X/..."Author's post-print on open access repository after an embargo period of between 12 months and 48 months" from SHERPA/RoMEO site (as at 4/01/18).
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