ON THE SPECTRUM OF TWISTED LAPLACIANS AND THE TEICHM ÜLLER REPRESENTATION
Résumé
Given a compact hyperbolic surface X = Γ\H 2 and a linear nonunitary representation : Γ → GL(V), we investigate the spectrum of the twisted Laplacian ∆ acting on sections of the associated flat vector bundle E → X. We show that this non self-adjoint operator has its spectrum inside a parabola related to a critical exponent δ of the representation. In the case where is of Teichmüller type we then exhibit explicit parabolic regions determined by another constant δ 0 with an asymptotic spectral density which improves Weyl's law by a power factor. Both δ and δ 0 are uniquely determined by the so-called "Manhattan curve" related to the representation .
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)