Geometric Analysis of Hyperbolic Differential Equations: An Introduction

A self-contained presentation of the tools of Lorentzian geometry necessary to access recent works in mathematical relativity.

S. Alinhac (Author)

9780521128223, Cambridge University Press

Paperback, published 20 May 2010

130 pages
22.9 x 15.2 x 0.7 cm, 0.19 kg

'This book provides an excellent introduction to nonlinear wave equations, and it can be recommended to anyone who wants to access the recent mathematical literature on this subject.' Zentralblatt MATH

Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.

Preface
1. Introduction
2. Metrics and frames
3. Computing with frames
4. Energy inequalities and frames
5. The good components
6. Pointwise estimates and commutations
7. Frames and curvature
8. Nonlinear equations, a priori estimates and induction
9. Applications to some quasilinear hyperbolic problems
References
Index.

Subject Areas: Relativity physics [PHR], Geometry [PBM]