Conformal maps and the Riemann mapping theorem
A conformal map is one that preserves angles. In the case of mappings from one connected domain in \(\mathbb {C}\) to another, such a map is holomorphic, or else its complex conjugate is holomorphic.
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Richard Beals Roderick S. C. Wong
Explorations in Complex Functions
Graduate Texts in Mathematics
287
Graduate Texts in Mathematics Series Editors Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Editors Alejandro Adem, University of British Columbia David Eisenbud, University of California, Berkeley & MSRI Brian C. Hall, University of Notre Dame Patricia Hersh, University of Oregon J. F. Jardine, University of Western Ontario Jeffrey C. Lagarias, University of Michigan Eugenia Malinnikova, Stanford University Ken Ono, University of Virginia Jeremy Quastel, University of Toronto Barry Simon, California Institute of Technology Ravi Vakil, Stanford University Steven H. Weintraub, Lehigh University Melanie Matchett Wood, Harvard University
Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.
More information about this series at http://www.springer.com/series/136
Richard Beals Roderick S. C. Wong •
Explorations in Complex Functions
123
Richard Beals Department of Mathematics Yale University New Haven, CT, USA
Roderick S. C. Wong Department of Mathematics City University of Hong Kong Kowloon, Hong Kong
ISSN 0072-5285 ISSN 2197-5612 (electronic) Graduate Texts in Mathematics ISBN 978-3-030-54532-1 ISBN 978-3-030-54533-8 (eBook) https://doi.org/10.1007/978-3-030-54533-8 Mathematics Subject Classification: 30-01, 33-01, 30D35, 33E05, 11M06 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springe
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