We construct spectrum of the Laplacian on compact anti-de Sitter manifolds. In contrast to the classical setting where the nonzero discrete spectrum varies on the Teichmüler space of a compact Riemann surface, this infinite set of eigenvalues is stable under any small deformation of geometric structures. More generally, we discuss joint eigenfunctions for a system of canonical differential operatators on locally symmetric spaces with indefinite metric. This is a joint work with Fanny Kassel.
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© Toshiyuki Kobayashi