04010nam 22008055 450 99646659020331620200704151946.03-540-36074-310.1007/b84244(CKB)1000000000229420(SSID)ssj0000321279(PQKBManifestationID)12081773(PQKBTitleCode)TC0000321279(PQKBWorkID)10262447(PQKB)10854765(DE-He213)978-3-540-36074-2(MiAaPQ)EBC6298431(MiAaPQ)EBC5585594(Au-PeEL)EBL5585594(OCoLC)466113426(PPN)155174452(EXLCZ)99100000000022942020100806d2002 u| 0engurnn|008mamaatxtccrAnalytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral[electronic resource] /by Hervé M. Pajot1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (VIII, 119 p.) Lecture Notes in Mathematics,0075-8434 ;1799Bibliographic Level Mode of Issuance: Monograph3-540-00001-1 Includes bibliographical references (pages 115-118) and index.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.Lecture Notes in Mathematics,0075-8434 ;1799Mathematical analysisAnalysis (Mathematics)GeometryMeasure theoryFunctions of complex variablesFourier analysisAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Mathematical analysis.Analysis (Mathematics).Geometry.Measure theory.Functions of complex variables.Fourier analysis.Analysis.Geometry.Measure and Integration.Functions of a Complex Variable.Fourier Analysis.515/.42Pajot Hervé Mauthttp://id.loc.gov/vocabulary/relators/aut1060269MiAaPQMiAaPQMiAaPQBOOK996466590203316Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral2512070UNISA