Riemannian Geometry and Geometric Analysis (Universitext) - Softcover

Jost, Jurgen

9783540773405: Riemannian Geometry and Geometric Analysis (Universitext)

Softcover

ISBN 10: 3540773401 ISBN 13: 9783540773405

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2008

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This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. This new edition introduces and explains the ideas of the parabolic methods that have recently found such spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.

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Review

From the reviews of the sixth edition:

“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. This sixth edition contains a deeper study of the spectrum of the Laplace operator and its relation to the geometry of the underlying Riemannian manifold.” (M. Kunzinger, Monatshefte f�r Mathematik, Vol. 171 (3-4), September, 2013)

“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)

Synopsis

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. Besides several smaller additions, reorganizations, corrections, and a systematic bibliography, the main new features of the 4th edition are a systematic introduction to Kahler geometry and the presentation of additional techniques from geometric analysis. 'This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. The book is made more interesting by the perspectives in various sections' - "Math".

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