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arXiv · 1907.05723

Some geometric properties of Riemann's non-differentiable function

Daniel Eceizabarrena
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Abstract

Riemann's non-differentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory in experiments related to the binormal flow or the vortex filament equation. In this setting, we analyse certain geometric properties of its image in $\mathbb{C}$. The objective of this note is to assert that the Hausdorff dimension of its image is no larger than 4/3 and that it has nowhere a tangent.

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Daniel Eceizabarrena. 2019-07-12. Some geometric properties of Riemann's non-differentiable function. https://doi.org/10.1016/j.crma.2019.10.007

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