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Physics on Manifolds - Proceedings of the International Colloquium in honour of Yvonne Choquet-Bruhat, Paris, June 3-5, 1992 (Paperback, Softcover reprint of the original 1st ed. 1994)
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Physics on Manifolds - Proceedings of the International Colloquium in honour of Yvonne Choquet-Bruhat, Paris, June 3-5, 1992 (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: Mathematical Physics Studies, 15
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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.
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