Global Riemannian Geometry: Curvature and Topology
This book contains a clear exposition of two contemporary topics in modern differential geometry:distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature
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Ana Hurtado Steen Markvorsen Maung Min-Oo Vicente Palmer
Global Riemannian Geometry: Curvature and Topology Second Edition
Advanced Courses in Mathematics CRM Barcelona Centre de Recerca Matemàtica Managing Editor: David Romero i Sànchez
More information about this series at http://www.springer.com/series/5038
Ana Hurtado • Steen Markvorsen • Maung Min-Oo Vicente Palmer
Global Riemannian Geometry: Curvature and Topology Second Edition
Ana Hurtado Departamento de Geometría y Topología Universidad de Granada Granada, Spain
Steen Markvorsen DTU Compute Technical University of Denmark Kgs. Lyngby, Denmark
Maung Min-Oo Department of Mathematics & Statistics McMaster University Hamilton, ON, Canada
Vicente Palmer Departament de Matemàtiques Universitat Jaume I Castelló de la Plana, Spain
ISSN 2297-0304 ISSN 2297-0312 (electronic) Advanced Courses in Mathematics - CRM Barcelona ISBN 978-3-030-55292-3 ISBN 978-3-030-55293-0 (eBook) https://doi.org/10.1007/978-3-030-55293-0 © Springer Nature Switzerland AG 2003, 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 book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents Preface to the first edition, 2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Preface to the second edition, 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Distance Geometric Analysis on Manifolds Ana Hurtado, Steen Markvorsen, and Vicente Palmer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Appetizer and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 The Comparison Setting and Preliminaries . . . . . . .
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