This is an announcement for the paper “Images of nowhere differentiable Lipschitz maps of $[0,1]$ into $L_1[0,1]$” by Florin Catrinahttps://arxiv.org/find/math/1/au:+Catrina_F/0/1/0/all/0/1, Mikhail I. Ostrovskiihttps://arxiv.org/find/math/1/au:+Ostrovskii_M/0/1/0/all/0/1.

Abstract: The main result: for every $m\in\mathbb{N}$ and $omega>0$ there exists an isometric embedding $F: [0,1]\rightarrow L_1[0,1]$ which is nowhere differentiable, but for each $t\in[0,1]$ the image $F_t$ is an $m$-times continuously differentiable function with absolute values of all of its $m$ derivatives bounded from above by $\omega$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1705.08916