Sphere Packings in Hyperbolic Space: Periodicity and Continuity
نویسنده
چکیده
We prove that given a fixed radius r, the set of isometry-invariant probability measures supported on “periodic” radius-r sphere packings in hyperbolic space Hn is dense in the space of all isometry-invariant probability measures on the space of radius-r sphere packings when n = 2, 3. By a periodic packing, we mean one with cofinite symmetry group. As a corollary, we prove the maximum density achieved by isometryinvariant probability measures on the space of radius r-packings is the supremum of densities of periodic packings. We also show that the maximum density function varies continuously with radius in every dimension. This extends previous results of the author. MSC: 52A40, 52C26, 52C23
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