Examples of $2$-unrectifiable normal currents

Abstract

We construct new examples of normal (metric) currents using inverse systems of cube complexes. For any $N\ge 2$ we provide examples of $N$-dimensional normal currents whose associated vector fields are simple, and whose supports are purely $2$-unrectifiable and have Nagata dimension $N$. We show that in $l^{\infty }$ normal currents can be realized as limits in the flat distance of currents associated to cube complexes.

Minor corrections; Q2 will be answered in a following paper

References in corpus (1)

• Derivations and Alberti representations