Author	Pajot, Hervรฉ. author
Title	Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / by Hervรฉ Pajot
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b84244
Descript	VIII, 119 p. online resource

Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevรฉ problem

Preface -- Notations and conventions -- Some geometric measures theory -- Jones' traveling salesman theorem -- Menger curvature -- The Cauchy singular integral operator on Ahlfors-regular sets -- Analytic capacity and the Painlevรฉ Problem -- The Denjoy and Vitushkin conjectures -- The capacity $gamma (+)$ and the Painlevรฉ Problem -- Bibliography -- Index

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Fourier analysis
5. Functions of complex variables
6. Measure theory
7. Geometry
8. Mathematics
9. Analysis
10. Geometry
11. Measure and Integration
12. Functions of a Complex Variable
13. Fourier Analysis