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Universitext

Riemannian Geometry and Geometric Analysis

Authors: Jost, Jürgen

  • Continues to lead its readers to some of the hottest topics of contemporary research
  • Each chapter now includes additional basic exercises to test the reader’s understanding
  • Features new material on Ricci curvature
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eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-61860-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-61859-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. 
The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature.

From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews

“For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik




About the authors

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalflächen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.





Reviews

“The present volume ends with two appendices (on linear elliptic partial differential equations and topological results about fundamental groups and covering spaces) and a rich bibliography of 454 items, including some classical books and papers. All the material, written in a clear and precise style, is carefully developed, many examples supporting the understanding. In the reviewer’s opinion, this is an excellent book, a very useful addition to any good library.” (Gabriel Eduard Vilcu, zbMATH 1380.53001, 2018)

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Table of contents (12 chapters)

  • Chapter 1 Riemannian Manifolds

    Jost, Jürgen

    Pages 1-49

  • Chapter 2 Lie Groups and Vector Bundles

    Jost, Jürgen

    Pages 51-114

  • Chapter 3 The Laplace Operator and Harmonic Differential Forms

    Jost, Jürgen

    Pages 115-162

  • Chapter 4 Connections and Curvature

    Jost, Jürgen

    Pages 163-232

  • Chapter 5 Geometry of Submanifolds

    Jost, Jürgen

    Pages 233-249

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-319-61860-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-319-61859-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Geometry and Geometric Analysis
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-61860-9
DOI
10.1007/978-3-319-61860-9
Softcover ISBN
978-3-319-61859-3
Series ISSN
0172-5939
Edition Number
7
Number of Pages
XIV, 697
Number of Illustrations
15 b/w illustrations, 4 illustrations in colour
Additional Information
Originally published by Springer-Verlag Berlin Heidelberg, 1995, 1998, 2002, 2005, 2008, 2011
Topics