10-109 Abderemane Morame, Francoise Truc
Eigenvalues of Laplacian with constant magnetic field on noncompact hyperbolic surfaces with finite area (201K, pdf) Jul 26, 10
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Abstract. We consider a magnetic Laplacian \$-\Delta_A=(id+A)^\star (id+A)\$ on a noncompact hyperbolic surface M 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. n 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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