Riemannian Geometry and Geometric Analysis

In its updated 4th Edition, this classic reference offers some of the hottest topics of contemporary mathematical research, including a systematic introduction to Kähler geometry and the presentation of additional techniques from geometric analysis.

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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.