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

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 $dA=0.$

References in corpus (3)

• Essential self-adjointness for semi-bounded magnetic Schrödinger operators on non-compact manifolds
• Spectral analysis of magnetic Laplacians on conformally cusp manifolds
• Magnetic bottles on geometrically finite hyperbolic surfaces