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

David Borthwick; Colin Guillarmou

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arXiv · 1303.7471

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

David Borthwick·Colin Guillarmou

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Abstract

On geometrically finite hyperbolic manifolds $Γ\backslash H^{d}$, 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 $R\to \infty$. In particular, if the parabolic subgroups of $Γ$ satisfy a certain Diophantine condition, the bound is $N(R)= O(R^d (\log R)^{d+1})$.

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David Borthwick, Colin Guillarmou. 2013-04-17. Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds. https://arxiv.org/abs/1303.7471

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