Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds

作者：Borthwick D^*; Guillarmou C^*

来源：Journal of the European Mathematical Society, 2016, 18(5): 997-1041.

DOI：10.4171/JEMS/607

• Spectral geometry
• hyperbolic manifolds
• resonances

On geometrically finite hyperbolic manifolds Gamma\H-d, including those with non-maximal rank cusps, we give upper bounds on the number N(R) of resonances of the Laplacian in disks of size R as R -> infinity. In particular, if the parabolic subgroups of Gamma satisfy a certain Diophantine condition, the bound is N(R) = O(R-d (log R)(d+1)).

• 出版日期2016