T. Kobayashi. Intrinsic sound of anti-de Sitter manifolds, Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics & Statistics, vol. 191, Springer, 2016, pp. 83-99, DOI: 10.1007/978-981-10-2636-2_6. arXiv: 1609.05986..

As is well-known for compact Riemann surfaces, eigenvalues of the Laplacian are distributed discretely and most of eigenvalues vary viewed as functions on the Teichmüller space. We discuss a new feature in the Lorentzian geometry, or more generally, in pseudo-Riemannian geometry. One of the distinguished features is that L2-eigenvalues of the Laplacian may be distributed densely in R in pseudo-Riemannian geometry. For three-dimensional anti-de Sitter manifolds, we also explain another feature proved in joint with F. Kassel [Adv. Math. 2016] that there exist countably many L2-eigenvalues of the Laplacian that are stable under any small deformation of anti-de Sitter structure. Partially supported by Grant-in-Aid for Scientific Research (A) (25247006), Japan Society for the Promotion of Science.

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