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Abstrakty
For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for $D ⊂ ℂ^n$, n ≥ 3, we have $h_D ≡ ϰ_D$. Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that $h_{D₁ × D₂}$ iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ \ {0}. In particular, there are domains D ⊂ ℂ² for which $h_D ≢ ϰ_D$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
289-294
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-10-03
Twórcy
autor
- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
- [Cho] K. S. Choi, Injective hyperbolicity of product domain, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 5 (1998), 73-78.
- [Hah] K. T. Hahn, Some remark on a new pseudo-differential metric, Ann. Polon. Math. 39 (1981), 71-81.
- [Jar-Pfl] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter Exp. Math. 9, de Gruyter, Berlin, 1993.
- [Ove] M. Overholt, Injective hyperbolicity of domains, Ann. Polon. Math. 62 (1995), 79-82.
- [Roy] H. L. Royden, Remarks on the Kobayashi metric, in: Several Complex Variables, II, Lecture Notes in Math. 189, Springer, 1971, 125-137.
- [Two-Win] P. Tworzewski and T. Winiarski, Continuity of intersection of analytic sets, Ann. Polon. Math. 42 (1983), 387-393.
- [Ves] E. Vesentini, Injective hyperbolicity, Ricerche Mat. 36 (1987), 99-109.
- [Vig] J.-P. Vigué, Une remarque sur l'hyperbolicité injective, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 83 (1989), 57-61.
Typ dokumentu
Bibliografia
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