Inner Carathéodory completeness of Reinhardt domains
Zwonek, Włodzimierz
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 12 (2001), p. 153-157 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

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

Si presenta la descrizione di domini di Reinhardt limitati e pseudo-convessi, che sono completi per la distanza interna di Carathéodory.

Publié le : 2001-09-01
@article{RLIN_2001_9_12_3_153_0,
     author = {W\l odzimierz Zwonek},
     title = {Inner Carath\'eodory completeness of Reinhardt domains},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {12},
     year = {2001},
     pages = {153-157},
     zbl = {1072.32017},
     mrnumber = {1898456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2001_9_12_3_153_0}
}

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, Tome 12 (2001) pp. 153-157. http://gdmltest.u-ga.fr/item/RLIN_2001_9_12_3_153_0/

[1] Barth, T.J., Some counterexamples concerning intrinsic distances. Proc. Amer. Math. Soc., 66(1), 1977, 49-53. | MR 454078 | Zbl 0331.32019

[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. | MR 1292574 | Zbl 0813.32024

[3] Fu, S., On completeness of invariant metrics of Reinhardt domains. Arch. Math., 63, 1994, 166-172. | MR 1289299 | Zbl 0815.32001

[4] Jarnicki, M. - Pflug, P., The simplest example for the noninnerness of the Carathéodory distance. Resultate Math., 18, no. 1-2, 1990, 57-59. | MR 1066642 | Zbl 0709.32015

[5] Jarnicki, M. - Pflug, P., Invariant Distances and Metrics in Complex Analysis. Walter de Gruyter, 1993. | MR 1242120 | Zbl 0789.32001

[6] Pflug, P., About the Carathéodory completeness of all Reinhardt domains. In: G. Zapata (ed.), Functional Analysis, Holomorphy and Approximation Theory II. North-Holland, Amsterdam 1984, 331-337. | MR 771335 | Zbl 0536.32001

[7] Vigué, J.P., La distance de Carathéodory n’est pas intérieure. Resultate Math., 6, no. 1, 1983, 100-104. | MR 714663 | Zbl 0552.32022

[8] Zwonek, W., On hyperbolicity of pseudoconvex Reinhardt domains. Arch. Math., 72, 1999, 304-314. | MR 1678013 | Zbl 0938.32003

[9] Zwonek, W., On Bergman completeness of pseudoconvex Reinhardt domains. Ann. de la Faculté des Sciences de Toulouse, 8(3), 1999, 537-552. | MR 1751175 | Zbl 0963.32003

[10] Zwonek, W., On Carathéodory completeness of pseudoconvex Reinhardt domains. Proc. Amer. Math. Soc., 128(3), 2000, 857-864. | MR 1646214 | Zbl 0939.32025

[11] Zwonek, W., Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions. Diss. Math., 388, 2000, 1-103. | MR 1785672 | Zbl 0965.32004