Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral (Lecture Notes in Mathematics)

HervAc M. Pajot

ISBN 10: 3540000011 / ISBN 13: 9783540000013

Editore: Springer 2008-06-13, 2008

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Codice articolo 6666-IUK-9783540000013

Dati bibliografici

• Titolo: Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral (Lecture Notes in Mathematics)
• Editore: Springer 2008-06-13
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3540000011
• ISBN 13: 9783540000013
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.