On packing of Minkowski balls. II

2023/02/03 by Glazunov, Nikolaj
#11H06 #52C05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.01644

Abstract

This is the continuation of the author's ArXiv presentation "On packing of Minkowski balls. I". In section 2 we investigate lattice packings of Minkowski balls and domains. By results of the proof of Minkowski conjecture about the critical determinant we devide the balls and domains on 3 classes: Minkowski, Davis and Chebyshev-Cohn. The optimal lattice packings of the balls and domains are obtained. The minimum areas of hexagons inscribed in the balls and domains and circumscribed around their are given. Direct limits of direct systems of Minkowski balls and domains and their critical lattices are calculated.

Related

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• On packing of Minkowski balls. I
• On direct and inverse limits of Minkowski's balls, domains, and their critical lattices
• On coverings by Minkowski balls in the plane and a duality
• On Minkowksi's bound for lattice-packings