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

Abstract

top
On geometrically finite hyperbolic manifolds Γ 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 . 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 ) .

How to cite

top

Borthwick, 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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.