On Small Gaps in the Length Spectrum
On Small Gaps in the Length Spectrum
复制标题
关于长度谱中的小间隙
DOI：
10.3934/jmd.2016.10.339
复制
发表时间：
2016
影响因子：
1.1
通讯作者：
D. Jakobson
中科院分区：
文献类型：
--
作者：
D. Dolgopyat;D. Jakobson
我们讨论的上限和下限的差距的大小，
负曲流形的长度谱对于代数流形
生成元的基本群，我们建立指数的存在性
差距的下限。另一方面，我们表明，
任意小的间隙是拓扑通用的：这是建立在两个
常负曲率的曲面（定理3.1）和
负曲度量（定理4.1）。尽管任意小的间隙
从拓扑学上讲，这是合理的，差距不是太小，几乎
每一个公制第5节给出了这方面的一个结果。
We discuss upper and lower bounds for the size of gaps in the
length spectrum of negatively curved manifolds. For manifolds with algebraic
generators for the fundamental group, we establish the existence of exponential
lower bounds for the gaps. On the other hand, we show that the existence
of arbitrarily small gaps is topologically generic: this is established both for
surfaces of constant negative curvature (Theorem 3.1) and for the space of
negatively curved metrics (Theorem 4.1). While arbitrarily small gaps are
topologically generic, it is plausible that the gaps are not too small for almost
every metric. One result in this direction is presented in Section 5.