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Construction of labyrinths in pseudoconvex domains

Abstract : 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.
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https://hal-amu.archives-ouvertes.fr/hal-03466291
Contributor : Stéphane Charpentier Connect in order to contact the contributor
Submitted on : Saturday, December 4, 2021 - 11:53:27 PM
Last modification on : Tuesday, January 4, 2022 - 5:45:34 AM

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

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