Kobayashi-Royden vs. Hahn pseudometric in ℂ²

• Autorzy: Witold Jarnicki
• Języki publikacji: EN

Abstrakty

EN

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

EN

Hahn pseudometric   Kobayashi pseudometric  

Kategorie tematyczne

• 32F45: Invariant metrics and pseudodistances

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 3
• Strony: 289-294

Daty

wydano

2000

otrzymano

2000-10-03

Twórcy

autor

Witold Jarnicki

• 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.