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arXiv · 0910.5283

Resonance free regions for nontrapping manifolds with cusps

Kiril Datchev
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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This paper has been withdrawn because of a mistake in Lemma 7.4.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.

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Kiril Datchev. 2009-10-28. Resonance free regions for nontrapping manifolds with cusps. https://arxiv.org/abs/0910.5283

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