Lattice points in stretched finite type domains

Abstract

We study an optimal stretching problem, which is a variant lattice point problem, for convex domains in ${\mathbb{R}}^d$ ($d\ge 2$) with smooth boundary of finite type that are symmetric with respect to each coordinate hyperplane/axis. We prove that optimal domains which contain the most positive (or least nonnegative) lattice points are asymptotically balanced.