The Cauchy-Riemann Complex Integral Formulae and Neumann Problem
The method of integral representations is developed in order to establish 1. classical fundamental results of complex analysis both elementary and advanced, 2. subtle existence and regularity theorems for the Cauchy-Riemann equations on complex manifolds.
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The Cauchy-Riemann Complex
Aspects of Mathematics Edited by Klas Diederich
Vol. E 3: G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part B Vol. E 6: G. Faltings/G. Wustholz et al.: Rational Points* Vol. E 15: J.-P. Serre: Lectures on the Mordell-Weil Theorem Vol. E 16: K. Iwasaki/H. Kimura/S. Shimomura/M. Yoshida: From Gauss to Painleve Vol. E 19: R. Racke: Lectures on Nonlinear Evolution Equations Vol. E 21: H. Fujimoto: Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm Vol. E22: D. V. Anosov/A. A. Bolibruch: The Riemann-Hilbert Problem Vol. E 27: D. N. Akhiezer: Lie Group Actions in Complex Analysis Vol. E28: R. Gerard/H. Tahara: Singular Nonlinear Partial Differential Equations Vol. E30: R. Huber: Etale Cohomology of Rigid Analytic Varieties and Adic Spaces Vol. E32: M. Yoshida: Hypergeometric Functions, My Love Vol. E33: C. Faber/E. Looijenga (Eds.): Moduli of Curves and Abelian Varieties Vol. E34: I. Lieb/J. Michel: The Cauchy-Riemann Complex
* A Publication of the Max-Planck-Institut fiir Mathematik, Bonn
Ingo Lieb Joachim Michel
The Cauchy-Riemann Complex Integral Formulae and Neumann Problem
II vleweg
Prof. Dr. Jngo Lieb Rheinische Friedrich-Wilhelms-Universitat Bonn Mathematisches Institut BeringstraBe 6 D-53115 Bonn, Germany [email protected] Prof. Dr. Joachim Michel Laboratoire de Mathematiques Pures et Appliquees Joseph Liouville 50, rue Ferdinand Buisson F-62228 Calais Cedex, France [email protected] Prof. Dr. Klas Diederich (Series Editor) Bergische Universitiit - Gesamthochschule Wuppertal Fachbereich 7 - Mathematik GauBstraBe 20 D-42119 Wuppertal, Germany [email protected]
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First edition, March 2002 All rights reserved © Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweigjWiesbaden, 2002 Softcover reprint of the hardcover 1st edition 2002 Vieweg is a company in the specialist publishing group BertelsmannSpringer. www.vieweg.de
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Cover design: Ulrike Weigel, www.CorporateDesignGroup.de Printed on acid-free paper ISBN 978-3-322-91610-5 ISBN 978-3-322-91608-2 (eBook) DOI 10.1007/978-3-322-91608-2
ISSN 0179-2156
Hans Grauert gewidmet
Preface This book presents complex analysis of several variables from the point of view of the Cauchy-Riemann equations and integral representations. A more detailed description of our methods and main results can be found in the introduction. Here we only make some remarks on our aims and on the required background knowledge. Integral representation methods serve a twofold purpose: 1° they yield regularity results not easily obtained by other methods and 2°, along the way, they lead to a fairly simple development of parts of the classical theory of several complex varia
