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arXiv · 1004.5291

Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area

Abderemane Morame·Francoise Truc
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Abstract

We consider a magnetic Laplacian $-Δ_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM $ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$ satifies some quantified condition, the spectrum of $-Δ_A$ is discrete. In this case we prove that the counting function of the eigenvalues of $-Δ_{A}$ satisfies the classical Weyl formula, even when $dA=0. $

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Abderemane Morame, Francoise Truc. 2010-05-31. Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area. https://doi.org/10.1007/s11005-011-0489-6

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