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Pré-Publication, Document De Travail Année : 2022

ON THE SPECTRUM OF TWISTED LAPLACIANS AND THE TEICHM ÜLLER REPRESENTATION

Frédéric Naud
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Polyxeni Spilioti
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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 .
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Dates et versions

hal-03841745 , version 1 (07-11-2022)

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  • HAL Id : hal-03841745 , version 1

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Frédéric Naud, Polyxeni Spilioti. ON THE SPECTRUM OF TWISTED LAPLACIANS AND THE TEICHM ÜLLER REPRESENTATION. 2022. ⟨hal-03841745⟩
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