Abstract
Anti-de Sitter spacetime is a Cinfinity manifold diffeomorphic to R4, endowed with a Cinfinity metric of hyperbolic signature. However this spacetime is not globally hyperbolic, and the known results about the solution of the Cauchy problem for wave equations on Lorentzian manifolds do not apply, even for a small interval of time and even for linear equations. The author proves the global existence of a solution of the Cauchy problem for the Yang-Mills-Higgs equations on anti-de Sitter spacetime, under the condition that there is no radiation at timelike infinity, a condition that is explained mathematically.
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