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k-convexity in several complex variables

Hidetaka Hamada, Gabriela Kohr (2002)

Annales Polonici Mathematici

We define and investigate the notion of k-convexity in the sense of Mejia-Minda for domains in ℂⁿ and also that of k-convex mappings on the Euclidean unit ball.

Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Witold Jarnicki (2000)

Annales Polonici Mathematici

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 D ₁ × D ₂ 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 .

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