This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.

Klappentext

The role of the geometry of manifolds in space-time physics, and that of functional analysis in quantum mechanics and quantum field theory have become increasingly important. This is particularly true in the study of the global behaviour of solutions of differential systems on manifolds, and their implications to general relativity. Yvonne Choquet-Bruhat has contributed much to this exciting area of mathematical physics, and her work on the existence of solutions to Einstein's equations on differential manifolds of a general type has subsequently stimulated and inspired much important research. She has also played a pioneering role in the study of global problems, especially in gauge field theory and supergravity, and in the development of a theory of asymptotic gravitational and electromagnetic waves. The various contributions appearing in this volume, authored by eminent scientists, illustrate the latest developments in the many areas of contemporary physics which have greatly benefited from Choquet-Bruhat's work and influence. For mathematical physicists with an interest in relativity, quantum mechanics and field theory.

Inhalt
Table Des Matieres.- Relativistic dissipative fluids1.- Mathematical problems related to liquid crystalssuperconductors andsuperfluide 11.- Microcanonical action and the entropy of a rotating black hole23.- Problèmede Cauchy sur un cônoïde caractéristique. Applications à certains systèmes non linéaires d'origine physique35.- Recent progress on the Cauchy problem in general relativity49.- On some links between mathematical physics and physics in the context ofgeneral relativity59.- Functionalintegration.Amultipurpose tool67.- Generalized frames of references and intrinsic Cauchy problem in general relativity93.- Reducing Einstein's equations to an unconstrainedHamiltonian system on the cotangent bundle of Teichmüller space111.- Darboux transformations for a class of integrable systems innvariables153.- Group theoretical treatment offundamental solutions161.- On the regularity properties of the wave equation177.- Le problème de Cauchy linéaire et analytique pour un opérateur holomorphe et unsecond membre ramifié[Résumé] 193.- On Boltzmann equation195.- Star products and quantum groups203.- On asymptotic of solutions of a nonlinear elliptic equationin a cylindrical doma.i:r235.- Fundamental physics in universal space-time253.- Interaction of gravitational and electromagnetic waves in general relativity265.- Anti-self dual conformal structures on 4-manifolds[Résumé] 289.- Chaotic behavior in relativistic motion291.- Some results on non constant mean curvature solutions ofthe Einstein constraint equations295.- Levi condition for general systems.- Conditionsinvariantespour un systèmedu type conditions de Levi 309.- Black holes in supergravity.- Low-dimensional behaviour in the rotating driven cavity problem.- Some geometrical aspects of inhomogeneouselasticity.- Integrating the Kadomtsev-Petviashvili equation in the 1+3 dimensions via the generalised Monge-Ampère equation: an example of conditionedPainlevé test337.- Spinning mass endowed with electric charge andmagnetic dipole moment347.- Equations de Vlasov en théorie discrète353.- Convexity and symmetrization in classical and relativistic balance laws systems.