We study the spectral theory and the resolvent of the vector field generating the frame flow of closed hyperbolic three-dimensional manifolds on some family of anisotropic Sobolev spaces. We show the existence of a spectral gap and prove resolvent estimates using semiclassical methods.

中文翻译：

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双曲三流形上帧流的谱理论

我们研究了谱理论和矢量场的解析，在某些各向异性 Sobolev 空间族上生成封闭双曲三维流形的框架流。我们展示了光谱间隙的存在，并使用半经典方法证明了解析度估计。