## 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 *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.
Partially supported by
Grant-in-Aid for Scientific Research (A) (25247006), Japan
Society for the Promotion of Science.

[ DOI | arXiv |
preprint version(pdf) ]

© Toshiyuki Kobayashi