Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral
Pajot, Hervé.
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / by Hervé Pajot. - VIII, 119 p. online resource. - Lecture Notes in Mathematics, 1799 0075-8434 ; . - Lecture Notes in Mathematics, 1799 .
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 Painlevé Problem -- The Denjoy and Vitushkin conjectures -- The capacity $gamma (+)$ and the Painlevé Problem -- Bibliography -- Index.
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 Painlevé problem.
9783540360742
10.1007/b84244 doi
Global analysis (Mathematics).
Geometry.
Mathematics.
Functions of complex variables.
Fourier analysis.
Analysis.
Geometry.
Measure and Integration.
Functions of a Complex Variable.
Fourier Analysis.
QA299.6-433
515
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / by Hervé Pajot. - VIII, 119 p. online resource. - Lecture Notes in Mathematics, 1799 0075-8434 ; . - Lecture Notes in Mathematics, 1799 .
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 Painlevé Problem -- The Denjoy and Vitushkin conjectures -- The capacity $gamma (+)$ and the Painlevé Problem -- Bibliography -- Index.
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 Painlevé problem.
9783540360742
10.1007/b84244 doi
Global analysis (Mathematics).
Geometry.
Mathematics.
Functions of complex variables.
Fourier analysis.
Analysis.
Geometry.
Measure and Integration.
Functions of a Complex Variable.
Fourier Analysis.
QA299.6-433
515