I would like to study the spectral theory of the Dirac Laplacian on a non-compact quotient of the hyperbolic plane by a discrete group (I am particularly interested in the simple case where the surface is a funnel).

Are there any references that are a good start? Thanks a lot for your help!

EDIT: As kindly pointed out in the comment below, the operator referred to above is a first-order operator with coefficients from a Clifford-algebra whose square is the "Laplacian" up to curvature terms.

  • $\begingroup$ Kind of obvious, but here's the first Google hit with some relevant keywords: mathcs.emory.edu/~davidb/spths.pdf $\endgroup$ Jul 21, 2013 at 21:05
  • $\begingroup$ @IgorKhavkine many thanks for your comments. As far as I understand the document is concerned with the Laplace Beltrami operator, I am interested in the Dirac Laplacian though. $\endgroup$
    – harlekin
    Jul 21, 2013 at 21:37
  • 3
    $\begingroup$ Do you mean a/the Dirac operator, a first-order Clifford-algebra coefficiented operator? (Whose square is the "Laplacian" up to curvature terms?) $\endgroup$ Jul 22, 2013 at 2:35
  • $\begingroup$ Please don't cross post. I'll close your version on MSE in a moment. If the question is not research level it will most likely be bounced to MSE anyway. $\endgroup$ Jul 22, 2013 at 7:44
  • $\begingroup$ Lax-Phillips... $\endgroup$
    – Asaf
    Jul 22, 2013 at 8:26


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