Riemannian Geometry and Geometric Analysis
(Sprache: Englisch)
This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.
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Produktinformationen zu „Riemannian Geometry and Geometric Analysis “
This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.
Klappentext zu „Riemannian Geometry and Geometric Analysis “
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 6 th 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." Mathematical Reviews
"...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
Inhaltsverzeichnis zu „Riemannian Geometry and Geometric Analysis “
Fundamental Material.- De Rham Cohomology and Harmonic Differential Forms.- Parallel Transport, Connections, and Covariant Derivatives.- Geodesics and Jacobi Fields.- A Short Survey on Curvature and Topology: Symmetric Spaces and Kähler Manifolds.- Morse Theory and Floer Homology.- Harmonic Maps between Riemannian Manifolds.- Harmonic Maps from Riemann Surfaces.- Variational Problems from Quantum Field Theory.- Appendix A: Linear Elliptic Partial Differential Equations.- Appendix B: Fundamental Groups and Covering Spaces.- Bibliography.- Index.
Autoren-Porträt von Jürgen Jost
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.
Bibliographische Angaben
- Autor: Jürgen Jost
- 2011, 6. Aufl., 611 Seiten, 4 farbige Abbildungen, 12 Schwarz-Weiß-Abbildungen, Maße: 15,9 x 24 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3642212972
- ISBN-13: 9783642212970
Sprache:
Englisch
Rezension zu „Riemannian Geometry and Geometric Analysis “
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)
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