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

David Borthwick; Colin Guillarmou

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 5, page 997-1041
- ISSN: 1435-9855

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topBorthwick, David, and Guillarmou, Colin. "Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds." Journal of the European Mathematical Society 018.5 (2016): 997-1041. <http://eudml.org/doc/277647>.

@article{Borthwick2016,

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

author = {Borthwick, David, Guillarmou, Colin},

journal = {Journal of the European Mathematical Society},

keywords = {spectral geometry; hyperbolic manifolds; resonances; spectral geometry; hyperbolic manifolds; resonances},

language = {eng},

number = {5},

pages = {997-1041},

publisher = {European Mathematical Society Publishing House},

title = {Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds},

url = {http://eudml.org/doc/277647},

volume = {018},

year = {2016},

}

TY - JOUR

AU - Borthwick, David

AU - Guillarmou, Colin

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

JO - Journal of the European Mathematical Society

PY - 2016

PB - European Mathematical Society Publishing House

VL - 018

IS - 5

SP - 997

EP - 1041

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

LA - eng

KW - spectral geometry; hyperbolic manifolds; resonances; spectral geometry; hyperbolic manifolds; resonances

UR - http://eudml.org/doc/277647

ER -

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