10-48 Abderemane Morame, Francoise Truc

Eigenvalues of Laplacian with constant magnetic field on noncompact hyperbolic surfaces with finite area (199K, pdf) Mar 14, 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. 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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