On Lempert functions in .
Ideal as an intersection of zero-dimensional ideals and the Noether exponent.
Kobayashi-Royden vs. Hahn pseudometric in ℂ²
For a domain D ⊂ ℂ the Kobayashi-Royden ϰ and Hahn h pseudometrics are equal iff D is simply connected. Overholt showed that for , n ≥ 3, we have . Let D₁, D₂ ⊂ ℂ. The aim of this paper is to show that iff at least one of D₁, D₂ is simply connected or biholomorphic to ℂ 0. In particular, there are domains D ⊂ ℂ² for which .
Concave domains with trivial biholomorphic invariants
It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.
On extremal holomorphically contractible families
We prove (Theorem 1.2) that the category of generalized holomorphically contractible families (Definition 1.1) has maximal and minimal objects. Moreover, we present basic properties of these extremal families.
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