Magnetic bottles on geometrically finite hyperbolic surfaces

Abderemane Morame (1) , Francoise Truc (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IF - Institut Fourier

We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic behaviour when the surface has an infinite area.

Keywords: spectral asymptotics; magnetic bottles; hyperbolic surfaces

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

Abderemane Morame, Francoise Truc. Magnetic bottles on geometrically finite hyperbolic surfaces. Journal of Geometry and Physics, 2009, 59 (7), pp.1079-1085. ⟨hal-00318791v2⟩