Hilbert几何中的谱半径与顺从性
Spectral Radius and Amenability in Hilbert Geometries
摘要：
我们研究了希尔伯特几何的谱底，证明了它为零当且仅当几何是可修正的，换句话说，当且仅当它允许一个Fölner序列。我们还表明，底部的频谱承认一个上界，这只取决于尺寸和这是底部的频谱的双曲几何的相同尺寸。本文从纯度规的观点，简要地研究了希尔伯特几何中的时球及其与谱底的关系。
英文摘要：
We study the bottom of the spectrum in Hilbert geometries, we show that it is zero if and only if the geometry is amenable, in other words if and only if it admits a Fölner sequence. We also show that the bottom of the spectrum admits an upper bound, which depends only on the dimension and which is the bottom of the spectrum of the Hyperbolic geometry of the same dimension. Horoballs, from a purely metric point of view, and their relation with the bottom of the spectrum in Hilbert geometries are briefly studied.
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