Minimum Action Curves in Degenerate Finsler Metrics Existence and Pr
Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type
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Matthias Heymann
Minimum Action Curves in Degenerate Finsler Metrics Existence and Properties
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
2134
More information about this series at http://www.springer.com/series/304
Matthias Heymann
Minimum Action Curves in Degenerate Finsler Metrics Existence and Properties
123
Matthias Heymann Mathematics Department Duke University Durham North Carolina, USA
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-17752-6 DOI 10.1007/978-3-319-17753-3
ISSN 1617-9692
(electronic)
ISBN 978-3-319-17753-3
(eBook)
Library of Congress Control Number: 2015942507 Mathematics Subject Classification (2010): 60F10 Large Deviations, 51-02 Geometry - Research exposition, 49J45 Calculus of variations and optimal control; optimization - Methods involving semicontinuity and convergence; relaxation Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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)
In memory of my beloved grandfather Julius Salzmann 11/03/1908 07/01/2009
Preface
This research monograph is an analytical treatment of a geometric problem that recently arose in an applied community [6, 7, 10] focused on developing numerical methods for understanding the pathways of rare transition events in stochastic dynamical systems with small noise. For years, it had been a reoccurring problem that the underlying mathematical framework, Wentzell-Freidlin theory [8], is typically formulated in terms of time-parameterized paths,
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