Geometric Mechanics

E-Book Overview

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.

E-Book Content

Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1798 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Waldyr Muniz Oliva Geometric Mechanics 13 Author Waldyr Muniz Oliva CAMGSD, Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa, Portugal E-mail: [email protected], [email protected] Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de Mathematics Subject Classification (2000): 70Hxx, 70G45, 37J60 ISSN 0075-8434 ISBN 3-540-44242-1 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whethe
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