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arXiv · 2405.12947

The hanging chain problem with respect to a circle

Rafael López
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Abstract

Let $\s^1$ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to $\s^1$. We describe the shape of these curves distinguishing if the curves lie in the inside or outside of $\s^1$. We extend the problem for energies that are powers to the distance to $\s^1$.

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Rafael López. 2024-05-21. The hanging chain problem with respect to a circle. https://arxiv.org/abs/2405.12947

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