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Physics on Manifolds

Proceedings of the International Colloquium in honour of Yvonne Choquet-Bruhat, Paris, June 3–5, 1992

  • Conference proceedings
  • © 1994

Overview

Editors:
  1. M. Flato

    1. Physique Mathématique, Université de Bourgogne, Dijon, France

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  2. R. Kerner

    1. Laboratoire de Gravitation et Cosmologie Relativistes, UPMC, Paris, France

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  3. A. Lichnerowicz

    1. Collège de France, Paris, France

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Part of the book series: Mathematical Physics Studies (MPST, volume 15)

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Table of contents (30 papers)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Conférences pleénières

    1. Relativistic Dissipative Fluids

      • A. M. Anile, G. Alí, V. Romano
      Pages 1-10

    2. Mathematical Problems Related to Liquid Crystals, Superconductors and Superfluids

      • Haïm Brezis
      Pages 11-21

    3. Microcanonical Action and the Entropy of a Rotating Black Hole

      • J. David Brown, James W. York Jr.
      Pages 23-34

    4. Problème De Cauchy Sur Un Cônoïde Caractéristique. Applications à Certains Systèmes Non Linéaires D’origine Physique

      • Francis Cagnac, Marcel Dossa
      Pages 35-47

    5. Recent Progress on the Cauchy Problem in General Relativity

      • Demetrios Christodoulou
      Pages 49-58

    6. On some links between mathematical physics and physics in the context of general relativity

      • Thibault Damour
      Pages 59-65

    7. Functional Integration a Multipurpose Tool

      • Cécile DeWitt-Morette
      Pages 67-91

    8. Generalized frames of references and intrinsic Cauchy problem in General Relativity

      • Giorgio Ferrarese, Carlo Cattani
      Pages 93-109

    9. Reducing Einstein’s Equations to an Unconstrained Hamiltonian System on the Cotangent Bundle of Teichmüller Space

      • Arthur E. Fischer, Vincent Moncrief
      Pages 111-151

    10. Darboux Transformations for a Class of Integrable Systems in n Variables

      • Chaohao Gu
      Pages 153-160

    11. Group Theoretical Treatment of Fundamental Solutions

      • N. H. Ibragimov
      Pages 161-175

    12. On the Regularity Properties of the Wave Equation

      • S. Klainerman, M. Machedon
      Pages 177-191

    13. Le problème de Cauchy linéaire et analytique pour un opérateur holomorphe et un second membre ramifié

      • Jean Leray
      Pages 193-193

    14. On Boltzmann Equation

      • P. L. Lions
      Pages 195-201

    15. Star Products and Quantum Groups

      • Carlos Moreno, Luis Valero
      Pages 203-234

    16. On asymptotic of solutions of a nonlinear elliptic equation in a cylindrical domain

      • O. A. Oleinik
      Pages 235-251

    17. Fundamental Physics in Universal Space-Time

      • Irving Segal
      Pages 253-264

    18. Interaction of Gravitational and Electromagnetic Waves in General Relativity

      • A. H. Taub
      Pages 265-287

    19. Anti-self dual conformal structures on 4-manifolds

      • Clifford Taubes
      Pages 289-289
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Keywords

About this book

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.

Editors and Affiliations

  • Physique Mathématique, Université de Bourgogne, Dijon, France

    M. Flato

  • Laboratoire de Gravitation et Cosmologie Relativistes, UPMC, Paris, France

    R. Kerner

  • Collège de France, Paris, France

    A. Lichnerowicz

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