Maximum Principles and Geometric Applications
This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented
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Luis J. Alías Paolo Mastrolia Marco Rigoli
Maximum Principles and Geometric Applications
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Luis J. Alías • Paolo Mastrolia • Marco Rigoli
Maximum Principles and Geometric Applications
123
Luis J. Alías Departamento de Matemáticas Universidad de Murcia Murcia, Spain
Paolo Mastrolia Dipartimento di Matematica Università degli Studi di Milano Milan, Italy
Marco Rigoli Dipartimento di Matematica Università degli Studi di Milano Milan, Italy
This work has been partially supported by MINECO/FEDER project MTM2012-34037 and Fundación Séneca project 04540/GERM/06, Spain. This research is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Región de Murcia, Spain, by Fundación Séneca, Regional Agency for Science and Technology. M. Rigoli has been partially supported by MEC Grant SAB2010-0073 and Fundación Séneca Grant 18883/IV/13, Programa Jiménez de la Espada. ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-24335-1 ISBN 978-3-319-24337-5 (eBook) DOI 10.1007/978-3-319-24337-5 Library of Congress Control Number: 2016930292 Mathematics Subject Classification: 58-02, 35B50, 53C20, 53C42, 35R01 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Contents
1
A Crash Course in Riemannian Geometry.. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.1 Moving Frames, Levi-Civita Connection Forms and the First Structure Equation .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.2 Covariant Derivative of Tensor Fields, Connection and Meaning of the First Structure Equation . . . . . .. . . . . . .
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