Riemannian Geometry and Geometric Analysis by Jürgen JostRiemannian Geometry and Geometric Analysis by Jürgen Jost

Riemannian Geometry and Geometric Analysis

byJürgen Jost

Paperback | July 28, 2011

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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 6thedition 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

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 num...
Title:Riemannian Geometry and Geometric AnalysisFormat:PaperbackDimensions:611 pages, 23.5 × 15.5 × 0.02 inPublished:July 28, 2011Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3642212972

ISBN - 13:9783642212970


Table of Contents

1. Riemannian Manifolds.- 2. Lie Groups and Vector Bundles.- 3. The Laplace Operator and Harmonic Differential Forms.- 4. Connections and Curvature.- 5. Geodesics and Jacobi Fields.- 6. Symmetric Spaces and K¨ahler Manifolds.- 7. Morse Theory and Floer Homology.- 8. Harmonic Maps between Riemannian Manifolds.- 9. Harmonic Maps from Riemann Surfaces.- 10. Variational Problems from Quantum Field Theory.- A. Linear Elliptic Partial Differential Equations.- A.1 Sobolev Spaces.- A.2 Linear Elliptic Equations.- A.3 Linear Parabolic Equations.- B. Fundamental Groups and Covering Spaces.- Bibliography.- Index.

Editorial Reviews

From the reviews of the sixth edition:"The present book is the sixth edition of the author's textbook on Riemannian geometry and geometric analysis. In general, it gives a synthesis of geometric and analytic methods in the study of Riemannian manifolds. . the book is well written. That is why I would recommend it to specialists in mathematics or physics and especially to Ph.D. students of differential geometry." (Miroslaw Doupovec, Zentralblatt MATH, Vol. 1227, 2012)