Existence of a Hall ray in higher dimensional Lagrange spectra

Yitwah Cheung, Zhijing Wendy Wang, Ruichong Zhang

Given any norm $\Vert \cdot {\Vert }_{{\mathbb{R}}^2}$ on ${\mathbb{R}}^2$, we prove that the Lagrange spectrum for $2$-vectors contains a Hall ray. Equivalently, every sufficiently small $\rho \ge 0$ o…