Periodicity and Circle Packings of the Hyperbolic Plane
Periodicity and Circle Packings of the Hyperbolic Plane
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双曲平面的周期性和圆堆积
DOI：
10.1023/b:geom.0000006580.47816.e9
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发表时间：
2003
影响因子：
0.5
通讯作者：
L. Bowen
中科院分区：
文献类型：
--
作者：
L. Bowen
我们证明了给定一个固定的半径r，在双曲平面的“周期”半径r-圆填充上支持的等距不变概率测度集在半径r-圆填充空间上的所有等距不变概率测度空间中是稠密的.所谓周期堆积，我们指的是具有上有限对称群的堆积。作为推论，我们证明了双曲平面上半径为r的填充空间上等距不变概率测度的最大密度是周期填充密度的上确界.我们还表明，最大密度函数随半径连续变化。
We prove that given a fixed radius r, the set of isometry-invariant probability measures supported on 'periodic' radius r-circle packings of the hyperbolic plane is dense in the space of all isometry-invariant probability measures on the space of radius r-circle packings. By a periodic packing, we mean one with cofinite symmetry group. As a corollary, we prove the maximum density achieved by isometry-invariant probability measures on a space of radius r-packings of the hyperbolic plane is the supremum of densities of periodic packings. We also show that the maximum density function varies continuously with radius.