双曲轨道曲面的等谱线性
Isospectral Finiteness of Hyperbolic Orbisurfaces
摘要：
我们讨论的问题isospectrality双曲orbisurfaces，检查之间的关系的几何orbisurface和拉普拉斯谱。我们表明，某些双曲orbisurfaces不能等谱，障碍涉及的奇点和我们的orbisurfaces属的数量。使用一个版本的Selberg迹公式的双曲orbisurfaces，我们表明，拉普拉斯谱确定的长度谱和阶的奇点，多达200多种可能性。相反，长度谱和奇点的阶数的知识决定了拉普拉斯谱。Huber定理的部分推广被用来证明双曲Orbisurfaces的等谱集具有有限基数，推广了McKean关于Riemann曲面的一个结果。
英文摘要：
We discuss questions of isospectrality for hyperbolic orbisurfaces, examining the relationship between the geometry of an orbisurface and its Laplace spectrum. We show that certain hyperbolic orbisurfaces cannot be isospectral, where the obstructions involve the number of singular points and genera of our orbisurfaces. Using a version of the Selberg Trace Formula for hyperbolic orbisurfaces, we show that the Laplace spectrum determines the length spectrum and the orders of the singular points, up to finitely many possibilities. Conversely, knowledge of the length spectrum and the orders of the singular points determines the Laplace spectrum. This partial generalization of Huber's theorem is used to prove that isospectral sets of hyperbolic orbisurfaces have finite cardinality, generalizing a result of McKean for Riemann surfaces.
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