Arkiv för Matematik

  • Ark. Mat.
  • Volume 37, Number 2 (1999), 409-423.

Riemann surfaces in fibered polynomial hulls

Marshall A. Whittlesey

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Let Δ be the closed unit disk in C, let Γ be the circle, let Π: Δ×C→Δ be projection, and let A(Δ) be the algebra of complex functions continuous on Δ and analytic in int Δ. Let K be a compact set in C2 such that Π(K)=Γ, and let Kλ≠{w∈C|(λ,w)∈K}. Suppose further that (a) for every λ∈Γ, Kλ is the union of two nonempty disjoint connected compact sets with connected complement, (b) there exists a function Q(λ,w)≠(w-R(λ))2-S(λ) quadratic in w with R,S∈A(Δ) such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ int Kλ, where S has only one zero in int Δ, counting multiplicity, and (c) for every λ∈Γ, the map ω→Q(λ,ω) is injective on each component of Kλ. Then we prove that К/K is the union of analytic disks 2-sheeted over int Δ, where К is the polynomial convex hull of K. Furthermore, we show that БК/K is the disjoint union of such disks.

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Ark. Mat., Volume 37, Number 2 (1999), 409-423.

Received: 15 January 1998
First available in Project Euclid: 31 January 2017

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1999 © Institut Mittag-Leffler


Whittlesey, Marshall A. Riemann surfaces in fibered polynomial hulls. Ark. Mat. 37 (1999), no. 2, 409--423. doi:10.1007/BF02412224.

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