Construction of labyrinths in pseudoconvex domains

Stéphane Charpentier (1) , Łukasz Kosiński (2)

1 I2M - Institut de Mathématiques de Marseille
2 UJ - Uniwersytet Jagielloński w Krakowie = Jagiellonian University

We build in a given pseudoconvex (Runge) domain D of C N an O(D)-convex set Γ, every connected component of which is a holomorphically contractible (convex) compact set, enjoying the property that any continuous path γ : [0, 1) → D with lim r→1 γ(r) ∈ ∂D and omitting Γ has infinite length. This solves a problem left open in a recent paper by Alarcón and Forstnerič.

Domaines: Analyse fonctionnelle [math.FA]

Stéphane Charpentier, Łukasz Kosiński. Construction of labyrinths in pseudoconvex domains. Mathematische Zeitschrift, 2020, 296 (3-4), pp.1021-1025. ⟨10.1007/s00209-020-02468-x⟩. ⟨hal-03466291⟩