Discrete Energy on Rectifiable Sets
This book aims to provide an introduction to the broad and dynamic subject of discrete energy problems and point configurations. Written by leading authorities on the topic, this treatise is designed with the graduate student and further explorers in mind
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Sergiy V. Borodachov Douglas P. Hardin Edward B. Saff
Discrete Energy on Rectifiable Sets
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Sergiy V. Borodachov Douglas P. Hardin Edward B. Saff •
Discrete Energy on Rectifiable Sets
123
•
Sergiy V. Borodachov Department of Mathematics Towson University Towson, MD, USA
Douglas P. Hardin Center for Constructive Approximation Department of Mathematics Vanderbilt University Nashville, TN, USA
Edward B. Saff Center for Constructive Approximation Department of Mathematics Vanderbilt University Nashville, TN, USA
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-0-387-84807-5 ISBN 978-0-387-84808-2 (eBook) https://doi.org/10.1007/978-0-387-84808-2 Mathematics Subject Classification (2010): 11K41, 28A78, 31C20, 52A40, 70F10, 74G65, 94B65 © Springer Science+Business Media, LLC, part of Springer Nature 2019 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 Springer imprint is published by the registered company Springer Science+Business Media, LLC part of Springer Nature. The registered company address is: 233 Spring Street, New York, NY 10013, U.S.A.
Equilibrium configurations for four different interacting systems of 4000 particles restricted to the surface of an embedded torus. Interactions are of the form 1=rs , where r is the distance between points and s ¼ 0:1; 1; 2, and 4, illustrating the Poppy-seed bagel theorem (Theorem 8.5.2)
To our wives, Viktoriia Malakhova Anne Hardin Loretta Saff, who have added true equilibrium to our lives.
Preface
Our goal is to provide an introduction to the study of minimal energy problems, particularly from the perspective of generating point configurations that provide useful discretizations of manifolds. In so doing, we hope to convey the beauty of the subject and to
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