Inner Carathéodory completeness of Reinhardt domains

Włodzimierz Zwonek

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2001)

  • Volume: 12, Issue: 3, page 153-157
  • ISSN: 1120-6330

Abstract

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We give a description of bounded pseudoconvex Reinhardt domains, which are complete for the Carathéodory inner distance.

How to cite

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Zwonek, Włodzimierz. "Inner Carathéodory completeness of Reinhardt domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 12.3 (2001): 153-157. <http://eudml.org/doc/252355>.

@article{Zwonek2001,
abstract = {We give a description of bounded pseudoconvex Reinhardt domains, which are complete for the Carathéodory inner distance.},
author = {Zwonek, Włodzimierz},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Carathéodory distance; Inner Carathéodory distance; Pseudoconvex Reinhardt domain; Carathédory distance; inner Carathédory distance; pseudoconvex Reinhardt domain},
language = {eng},
month = {9},
number = {3},
pages = {153-157},
publisher = {Accademia Nazionale dei Lincei},
title = {Inner Carathéodory completeness of Reinhardt domains},
url = {http://eudml.org/doc/252355},
volume = {12},
year = {2001},
}

TY - JOUR
AU - Zwonek, Włodzimierz
TI - Inner Carathéodory completeness of Reinhardt domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2001/9//
PB - Accademia Nazionale dei Lincei
VL - 12
IS - 3
SP - 153
EP - 157
AB - We give a description of bounded pseudoconvex Reinhardt domains, which are complete for the Carathéodory inner distance.
LA - eng
KW - Carathéodory distance; Inner Carathéodory distance; Pseudoconvex Reinhardt domain; Carathédory distance; inner Carathédory distance; pseudoconvex Reinhardt domain
UR - http://eudml.org/doc/252355
ER -

References

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  1. Barth, T.J., Some counterexamples concerning intrinsic distances. Proc. Amer. Math. Soc., 66(1), 1977, 49-53. Zbl0331.32019MR454078
  2. Belkhchicha, L. - Vigué, J.-P., Sur les espaces complets pour la distance de Carathéodory. Rend. Mat. Acc. Lincei, s. 9, v. 5, 1994, 189-192. Zbl0813.32024MR1292574
  3. Fu, S., On completeness of invariant metrics of Reinhardt domains. Arch. Math., 63, 1994, 166-172. Zbl0815.32001MR1289299DOI10.1007/BF01189891
  4. Jarnicki, M. - Pflug, P., The simplest example for the noninnerness of the Carathéodory distance. Resultate Math., 18, no. 1-2, 1990, 57-59. Zbl0709.32015MR1066642DOI10.1007/BF03323154
  5. Jarnicki, M. - Pflug, P., Invariant Distances and Metrics in Complex Analysis. Walter de Gruyter, 1993. Zbl0789.32001MR1242120DOI10.1515/9783110870312
  6. Pflug, P., About the Carathéodory completeness of all Reinhardt domains. In: G. Zapata (ed.), Functional Analysis, Holomorphy and Approximation Theory II. North-Holland, Amsterdam1984, 331-337. Zbl0536.32001MR771335DOI10.1016/S0304-0208(08)70835-1
  7. Vigué, J.P., La distance de Carathéodory n’est pas intérieure. Resultate Math., 6, no. 1, 1983, 100-104. Zbl0552.32022MR714663DOI10.1007/BF03323329
  8. Zwonek, W., On hyperbolicity of pseudoconvex Reinhardt domains. Arch. Math., 72, 1999, 304-314. Zbl0938.32003MR1678013DOI10.1007/s000130050337
  9. Zwonek, W., On Bergman completeness of pseudoconvex Reinhardt domains. Ann. de la Faculté des Sciences de Toulouse, 8(3), 1999, 537-552. Zbl0963.32003MR1751175
  10. Zwonek, W., On Carathéodory completeness of pseudoconvex Reinhardt domains. Proc. Amer. Math. Soc., 128(3), 2000, 857-864. Zbl0939.32025MR1646214DOI10.1090/S0002-9939-99-05226-0
  11. Zwonek, W., Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions. Diss. Math., 388, 2000, 1-103. Zbl0965.32004MR1785672DOI10.4064/dm388-0-1

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