Riemannian Geometry and Geometric Analysis
Description
The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes newmaterial, 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
Reviews / Votes
"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)More details
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Person
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.