Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
著者
書誌事項
Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
（Lecture notes in mathematics, 1799）
Springer, c2002
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注記
Bibliography: p. [115]-118
Includes index
内容説明・目次
内容説明
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 Painleve problem.
目次
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 Painleve Problem.- The Denjoy and Vitushkin conjectures.- The capacity $gamma (+)$ and the Painleve Problem.- Bibliography.- Index.
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