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 Teichmuller 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.
CITATION STYLE
Kobayashi, T. (2016). Intrinsic sound of anti-de sitter manifolds. In Springer Proceedings in Mathematics and Statistics (Vol. 191, pp. 83–99). Springer New York LLC. https://doi.org/10.1007/978-981-10-2636-2_6
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