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arXiv · 1608.01635

Unrectifiable normal currents in Euclidean spaces

Andrea Schioppa
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Abstract

We construct in $\mathbb{R}^{k+2}$ a $k$-dimensional simple normal current whose support is purely $2$-unrectifiable. The result is sharp because the support of a normal current cannot be purely $1$-unrectifiable and a $(k+1)$-dimensional normal current can be represented as an integral of $(k+1)$-rectifiable currents. This gives a negative answer to the (revised version) of a question of Frank Morgan (1984).

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Andrea Schioppa. 2016-08-04. Unrectifiable normal currents in Euclidean spaces. https://arxiv.org/abs/1608.01635

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