Local Optimality of the d-cube for Laplacian Eigenvalues

Braxton Osting, Robert Viator

For each $d\ge 2$ we prove that the unit $d$-cube ${\square }_d\subset {\mathbb{R}}^d$ is, on the class $\mathcal{P}$ of convex polytopes combinatorially equivalent to a $d$-cube, (i)…