Resonance free regions for nontrapping manifolds with cusps
Abstract
This paper has been withdrawn because of a mistake in Lemma 7.4. For a corrected version of the main theorem, as well as various further developments and applications, see arXiv:1210.7736. For nonpositively curved perturbations of parabolic cylinders we establish the existence of a logarithmically large resonance free region. We use an escape function construction in a compact part of the manifold and near infinity we use the method of complex scaling. To the author's knowledge this is the first proof of a large resonance free region for manifolds with cusps.
Keywords
Cite
@article{arxiv.0910.5283,
title = {Resonance free regions for nontrapping manifolds with cusps},
author = {Kiril Datchev},
journal= {arXiv preprint arXiv:0910.5283},
year = {2012}
}
Comments
This paper has been withdrawn because of a mistake in Lemma 7.4. For a corrected version of the main theorem, as well as various further developments and applications, see arXiv:1210.7736