On packing of Minkowski balls. II

TL;DR

This paper studies lattice packings of Minkowski balls and domains, classifies them into three types, and determines optimal packings, inscribed and circumscribed hexagon areas, and limits of their critical lattices.

Contribution

It classifies Minkowski balls and domains into three classes and derives their optimal lattice packings and critical lattice limits.

Findings

Classified Minkowski, Davis, and Chebyshev-Cohn balls and domains.

Derived optimal lattice packings for each class.

Calculated minimum inscribed and circumscribed hexagon areas.

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.