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Domains with several slits

  • Alexandru Aleman
  • William T. Ross
  • Nathan S. Feldman
Part of the Frontiers in Mathematics book series (FM)

Abstract

We now extend our main theorem (Theorem 6.2.1) to domains with several slits. More precisely, we consider domains of the form
$$ G = \mathbb{D}\backslash \bigcup\limits_{j = 1}^N {\gamma _{j,} } $$
(10.1.1)
where γ j are analytic arcs satisfying certain technical conditions. They are the following (see Figure 10.1 for an example):
  1. 1.

    Each γ j is a closed connected subset of a simple analytic open arc \( \hat \gamma _j \) which meets \( \mathbb{T} \) at a positive anggle. The arc \( \hat \gamma _j \) will be called an analytic continuation of γ j .

     
  2. 2.

    γ1, …, γ N are pairwise disjoint.

     
  3. 3.

    Each γ j has one end point λ j \( \mathbb{T} \) and γ j ∖ {λ j } ⊂ \( \mathbb{D} \)

     

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Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Alexandru Aleman
    • 1
  • William T. Ross
    • 2
  • Nathan S. Feldman
    • 3
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Department of Mathematics and Computer ScienceUniversity of RichmondRichmondUSA
  3. 3.Department of MathematicsWashington & Lee UniversityLexingtonUSA

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