# Spectral theory for Dirac Laplacian on a funnel

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.

• Kind of obvious, but here's the first Google hit with some relevant keywords: mathcs.emory.edu/~davidb/spths.pdf – Igor Khavkine Jul 21 '13 at 21:05
• @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. – harlekin Jul 21 '13 at 21:37
• Do you mean a/the Dirac operator, a first-order Clifford-algebra coefficiented operator? (Whose square is the "Laplacian" up to curvature terms?) – paul garrett Jul 22 '13 at 2:35
• 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. – Willie Wong Jul 22 '13 at 7:44
• Lax-Phillips... – Asaf Jul 22 '13 at 8:26