Covering the plane by rotations of a lattice arrangement of disks

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Suppose we put an $ε$-disk around each lattice point in the plane, and then we rotate this object around the origin for a set $Θ$ of angles. When do we cover the whole plane, except for a neighborhood of the origin? This is the problem we study in this paper. It is very easy to see that if $Θ= [0,2π]$ then we do indeed cover. The problem becomes more interesting if we try to achieve covering with a small closed set $Θ$.
8 pages

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Classical Analysis and ODEs, Metric Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/119428

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611800
 http://arxiv.org/abs/math/0611800

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arXiv