论文标题
萨尔纳克的光谱差距问题
Sarnak's spectral gap question
论文作者
论文摘要
我们在肯定的问题中回答了萨尔纳克（Sarnak）的问题，从2007年开始，确认帕特森 - 苏利文基地的特征功能是双曲线拉普拉斯（双曲线拉普拉斯）不变的独特的正方形集成函数。因此，后者具有最大光谱差距。我们证明了对拉普拉斯人的范围的进一步限制，这是来自Kleinian Sphere包装的广泛歧管。
We answer in the affirmative a question of Sarnak's from 2007, confirming that the Patterson-Sullivan base eigenfunction is the unique square-integrable eigenfunction of the hyperbolic Laplacian invariant under the group of symmetries of the Apollonian packing. Thus the latter has a maximal spectral gap. We prove further restrictions on the spectrum of the Laplacian on a wide class of manifolds coming from Kleinian sphere packings.
