Vitushkin’s Conjecture for Removable Sets

• Main Author: Dudziak, James J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2010.
• Series: Universitext,
• Subjects: Mathematics.; Functions of complex variables.; Functions of a Complex Variable.; Several Complex Variables and Analytic Spaces.

Vitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters...

Table of Contents:

• Removable Sets and Analytic Capacity
• Removable Sets and Hausdorff Measure
• Garabedian Duality for Hole-Punch Domains
• Melnikov and Verdera’s Solution to the Denjoy Conjecture
• Some Measure Theory
• A Solution to Vitushkin’s Conjecture Modulo Two Difficult Results
• The T(b) Theorem of Nazarov, Treil, and Volberg
• The Curvature Theorem of David and Léger.