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 |

SUMMARY

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

CONTENT

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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Fourier analysis
Functions of complex variables
Measure theory
Geometry
Mathematics
Analysis
Geometry
Measure and Integration
Functions of a Complex Variable
Fourier Analysis