11-128 Abderemane Morame, Francoise Truc

Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian (395K, PDF) Sep 9, 11

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Abstract. We consider a non compact, complete manifold M of finite area with cuspidal ends. The generic cusp is isomorphic to $X imes (1,+\infty )$ with metric $ds^2=(h+dy^2)/y^{2\delta}.$ X is a compact manifold equipped with the metric h. For a one-form A on M such that in each cusp A is a non exact one-form on the boundary at infinity, we prove that the magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ satisfies the Weyl asymptotic formula with sharp remainder. We deduce an upper bound for the counting function of the embedded eigenvalues of the Laplace-Beltrami operator $-\Delta =-\Delta_0 .$

Files: 11-128.src( cusps_eigen.pdf.mm , 11-128.keywords.mm )