具有尖点的非俘获流形的共振自由区
Resonance free regions for nontrapping manifolds with cusps
摘要：
这篇论文因为引理7.4中的一个错误而被撤回。对于主定理的修正版本，以及各种进一步的发展和应用，见arXiv：1210.7736。对于抛物柱面的非正弯曲扰动，我们建立了一个几何上大的无共振区的存在性。我们在流形的紧致部分使用逃逸函数构造，在无穷远处使用复尺度方法。据作者所知，这是第一次证明了一个大的共振自由区的流形尖点。
英文摘要：
This paper has been withdrawn because of a mistake in Lemma 7.4.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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