论文标题
在扭曲的Laplacians和Teichmüller代表
On the spectrum of twisted Laplacians and the Teichmüller representation
论文作者
论文摘要
我们认为拉普拉斯人的非单一曲折作用于紧凑的双曲线表面的平坦矢量束。这些非自我接合拉普拉斯人在复杂平面的抛物线内具有离散的频谱。对于Teichmüller类型的基本表面基本组的表示，我们研究了高能量极限，并确切地描述了大部分光谱的描述，在这些频谱中，Weyl的定律是根据曼哈顿曲线完全确定与TeichMüllerStemations完全确定的代表性指数的。我们的主要结果提供了对批量外部特征值的计数估计，对Weyl定律进行了多项式改进。
We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations of the fundamental group of the base surface which are of Teichmüller type, we investigate the high energy limit and give a precise description of the bulk of the spectrum where Weyl's law is satisfied in terms of critical exponents of the representations which are completely determined by the Manhattan curve associated to the Teichmüller deformation. Our main result provides a counting estimate for the eigenvalues outside the bulk with a polynomial improvement over Weyl's law.
