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arXiv · 2004.04783

Plane $R$-paths and their rectifiability property

Nico Lombardi·Marco Longinetti·Paolo Manselli·Adriana Venturi
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Abstract

A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable tangent cone to the path at $x$. These paths are locally descent curves of a nested family sets of reach $R$. Avoiding any smoothness requirements, we get angle estimate and not intersection property. Afterwards we are able to estimate the lenght and detour of this curve.

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Nico Lombardi, Marco Longinetti, Paolo Manselli, Adriana Venturi. 2020-04-09. Plane $R$-paths and their rectifiability property. https://arxiv.org/abs/2004.04783

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