Differentiability inside sets with upper Minkowski dimension one

Abstract

We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz function defined on the whole space is differentiable inside $S$. Such sets are constructed explicitly.

23 pages

Cited by in corpus (2)

• Structure of Porous Sets in Carnot Groups
• Differentiability of Lipschitz Functions in Lebesgue Null Sets