Injective hyperbolicity of domains

Marius Overholt

Annales Polonici Mathematici (1995)

  • Volume: 62, Issue: 1, page 79-82
  • ISSN: 0066-2216

Abstract

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The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.

How to cite

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Marius Overholt. "Injective hyperbolicity of domains." Annales Polonici Mathematici 62.1 (1995): 79-82. <http://eudml.org/doc/262854>.

@article{MariusOverholt1995,
abstract = {The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.},
author = {Marius Overholt},
journal = {Annales Polonici Mathematici},
keywords = {invariant metric; Kobayashi-Royden metric; Hahn metric; S-metric; Hahn pseudometric; Kobayashi-Royden pseudometric},
language = {eng},
number = {1},
pages = {79-82},
title = {Injective hyperbolicity of domains},
url = {http://eudml.org/doc/262854},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Marius Overholt
TI - Injective hyperbolicity of domains
JO - Annales Polonici Mathematici
PY - 1995
VL - 62
IS - 1
SP - 79
EP - 82
AB - The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.
LA - eng
KW - invariant metric; Kobayashi-Royden metric; Hahn metric; S-metric; Hahn pseudometric; Kobayashi-Royden pseudometric
UR - http://eudml.org/doc/262854
ER -

References

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  1. [1] K. T. Hahn, Some remarks on a new pseudo-differential metric, Ann. Polon. Math. 39 (1981), 71-81. Zbl0476.32031
  2. [2] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970, p. 77. 
  3. [3] C. D. Minda, The Hahn metric on Riemann surfaces, Kodai Math. J. 6 (1983), 57-69. Zbl0524.30013
  4. [4] Y.-T. Siu, All plane domains are Banach-Stein, Manuscripta Math. 14 (1974), 101-105. Zbl0294.32010
  5. [5] E. Vesentini, Injective hyperbolicity, Ricerche Mat., Suppl. Vol. 36 (1987), 99-109. 
  6. [6] J.-P. Vigué, Une remarque sur l'hyperbolicité injective, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 83 (1989), 57-61. Zbl0741.32019
  7. [7] J. Zhang, Metric S on holomorphy domain, Kexue Tongbao 33 (5) (1988), 353-356. Zbl0673.32024

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