双曲平面的直角六边形平铺

What's Next? Pub Date : 2015-03-18 DOI:10.1515/9780691185897-009

R. Kenyon

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引用次数: 1

摘要

研究了具有不同形状的直角六边形的双曲平面的平铺空间$\Omega$上的等距不变概率测度。证明了直角六边形上某自然测度族中的每个测度$\mu$，在$\Omega$上存在一个等距不变测度，其在瓷砖上的边际分布为$\mu$。

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Right-Angled Hexagon Tilings of the Hyperbolic Plane

We study isometry-invariant probability measures on the space $\Omega$ of tilings of the hyperbolic plane with right-angled hexagons of varying shapes. We prove that, for each measure $\mu$ in a certain natural family of measures on right-angled hexagons, there is an isometry-invariant measure on $\Omega$ whose marginal distribution on tiles is $\mu$.

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