The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between crystalline order and amorphous disorder. The present paper studies a generalisation of this concept to the unit sphere. It is shown that several well studied determinantal point processes are hyperuniform.2010 Mathematics Subject Classification. 60G55 (Primary) 11K38 65C05 82D30 (Secondary).

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This paper introduces a technique for proving the local optimality of packing configurations. Applying this technique to a general convex polygon, we prove that the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also locally optimal in the full space of packings.

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