The local optimality of the double lattice packing

TL;DR

This paper presents a technique to prove local optimality of packing configurations and demonstrates that a known double lattice packing for convex polygons is locally optimal among all packings.

Contribution

It introduces a new method for establishing local optimality and applies it to confirm the optimality of a specific double lattice packing for convex polygons.

Findings

The double lattice packing by Kuperberg and Kuperberg is locally optimal.

The technique can be applied to general convex polygons.

The proof confirms the local optimality in the full space of packings.

Abstract

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.