4
$\begingroup$

I would like to know what is known about the spectrum of the Laplace-Beltrami operator on 2-dimensional negatively curved surfaces of constant curvature.

For instance,

  • What is the spectrum of the Hyperbolic plane?

  • What is the Laplace-Beltrami operator and its spectrum for a compact surface of constant curvature $-1$ and genus $g\geq 2$?

Can anyone point me to the right reference?

1 Answers 1