Riemann surfaces in fibered polynomial hulls |
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Authors: | Marshall A Whittlesey |
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Institution: | (1) Department of Mathematics, Texas A&M University, 77843-3368 College Station, TX, USA |
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Abstract: | Let Δ be the closed unit disk in C, let Γ be the circle, let Π: Δ×C→Δ be projection, and letA(Δ) be the algebra of complex functions continuous on Δ and analytic in int Δ. LetK be a compact set in C2 such that Π(K)=Γ, and letK
λ≠{w∈C|(λ,w)∈K}. Suppose further that (a) for every λ∈Γ,K
λ 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 withR,S∈A(Δ) such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ intK
λ, whereS 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
ofK
λ. Then we prove that К/K is the union of analytic disks 2-sheeted over int Δ, where К is the polynomial convex hull ofK. Furthermore, we show that БК/K is the disjoint union of such disks. |
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