Overview
- Continues to lead its readers to some of the hottest topics of contemporary mathematical research
- Each chapter ends with a set of exercises
- The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other addition
Part of the book series: Universitext (UTX)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.
The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book.
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." MathematicalReviews
"...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH
Authors and Affiliations
About the author
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), Differentialgeometrie und MInimalflächen (1994, 2007, with J. Eschenburg), Dynamical Systems (2005), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.
Bibliographic Information
Book Title: Riemannian Geometry and Geometric Analysis
Authors: Jürgen Jost
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-642-21298-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
eBook ISBN: 978-3-642-21298-7Published: 28 July 2011
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 6
Number of Pages: XIII, 611
Number of Illustrations: 12 b/w illustrations, 4 illustrations in colour
Topics: Differential Geometry, Theoretical, Mathematical and Computational Physics