# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332925

Arkiv for Matematik, 37, (2), 409-423, 1998.1
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 C^{2}such that Π(\$K\$)=Γ, and let\$K\$_{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 with\$R,S∈A(Δ)\$such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ int\$K\$_{λ}, 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\$K\$_{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 of\$K\$. Furthermore, we show that БК/K is the disjoint union of such disks.
```@inproceedings{marshall1998riemann,
title={Riemann surfaces in fibered polynomial hulls},
author={Marshall A. Whittlesey},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203557142558734},
booktitle={Arkiv for Matematik},
volume={37},
number={2},
pages={409-423},
year={1998},
}
```
Marshall A. Whittlesey. Riemann surfaces in fibered polynomial hulls. 1998. Vol. 37. In Arkiv for Matematik. pp.409-423. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203557142558734.