论文标题
双曲线3个manifolds上框架流的光谱理论（与查尔斯·哈德菲尔德的附录有关）
Spectral theory of the frame flow on hyperbolic 3-manifolds (with an appendix by Charles Hadfield)
论文作者
论文摘要
我们研究了在某些各向异性Sobolev空间上产生封闭双曲线3维流形的媒介场的频谱理论和矢量场的分解。我们显示了光谱差距的存在，并使用半经典方法证明了分解估计。
We study the spectral theory and the resolvent of the vector field generating the frame flow of closed hyperbolic 3-dimensional manifolds on some family of anisotropic Sobolev spaces. We show the existence of a spectral gap and prove resolvent estimates using semiclassical methods.
