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arXiv · 1609.05986

Intrinsic sound of anti-de Sitter manifolds

Toshiyuki Kobayashi
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Abstract

As is well-known for compact Riemann surfaces, eigenvalues of the Laplacianbare 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 $L^2$-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 $L^2$-eigenvalues of the Laplacian that are stable under any small deformation of anti-de Sitter structure.

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Toshiyuki Kobayashi. 2016-09-20. Intrinsic sound of anti-de Sitter manifolds. https://arxiv.org/abs/1609.05986

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