Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian

Abstract : We consider a non compact, complete manifold {\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\bf{X}}\times ]1,+\infty [$ with metric $ds^2=(h+dy^2)/y^{2\delta}.$ {\bf{X}} is a compact manifold with nonzero first Betti number equipped with the metric $h.$ For a one-form $A$ on {\bf{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 $-\Delta =-\Delta_0 .$
Document type :
Journal articles
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00621070
Contributor : Francoise Truc <>
Submitted on : Wednesday, December 5, 2012 - 6:05:56 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on : Wednesday, March 6, 2013 - 5:10:34 PM

Files

040312C.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00621070, version 2
  • ARXIV : 1109.1995

Collections

Citation

Abderemane Morame, Francoise Truc. Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian. Mathematical Review Letters, 2012, 19 ((2)), pp 417-429. ⟨hal-00621070v2⟩

Share

Metrics

Record views

408

Files downloads

240