Wyniki wyszukiwania

1

Kobayashi-Royden vs. Hahn pseudometric in ℂ²

100%

Jarnicki W.

Annales Polonici Mathematici

|

2000

|

tom 75

|

nr 3

289-294

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 $h_D ≢ ϰ_D$.

2

Concave domains with trivial biholomorphic invariants

63%

Jarnicki W., Nikolov N.

Annales Polonici Mathematici

|

2002

|

tom 79

|

nr 1

63-66

EN

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.

3

On extremal holomorphically contractible families

51%

Jarnicki M., Jarnicki W., Pflug P.

Annales Polonici Mathematici

|

2003

|

tom 81

|

nr 2

183-199

EN

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.

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Jarnicki W.

1 Jarnicki M.

1 Nikolov N.

1 Pflug P.

1 2003

1 2002

1 2000

Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Concave domains with trivial biholomorphic invariants

On extremal holomorphically contractible families