Compactness of relatively isospectral sets of surfaces via conformal surgeries
Differential Geometry
2012-06-27 v1 Spectral Theory
Abstract
We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to reduce to the case of surfaces hyperbolic near infinity recently studied by Borthwick and Perry, or to the closed case by Osgood, Phillips and Sarnak if there are only cusps.
Keywords
Cite
@article{arxiv.1206.6077,
title = {Compactness of relatively isospectral sets of surfaces via conformal surgeries},
author = {Pierre Albin and Clara L. Aldana and Frédéric Rochon},
journal= {arXiv preprint arXiv:1206.6077},
year = {2012}
}
Comments
22 pages, 3 figures