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Journal Articles Letters in Mathematical Physics Year : 2011

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

Abderemane Morame
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Francoise Truc

Abstract

We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ 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 $-\Delta_A$ is discrete. In this case we prove that the counting function of the eigenvalues of $-\Delta_{A}$ satisfies the classical Weyl formula, even when $dA=0. $
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Dates and versions

hal-00462411 , version 1 (09-03-2010)
hal-00462411 , version 2 (10-05-2010)

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Abderemane Morame, Francoise Truc. Eigenvalues of Laplacian with constant magnetic field on non-compact hyperbolic surfaces with finite area. Letters in Mathematical Physics, 2011, 97 (2), pp.203-211. ⟨10.1007/s11005-011-0489-6⟩. ⟨hal-00462411v2⟩
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