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arXiv · 1202.0504

For which positive $p$ is the integral Menger curvature $\mathcal{M}_{p}$ finite for all simple polygons?

Sebastian Scholtes
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Abstract

In this brief note we show that the integral Menger curvature $\mathcal{M}_{p}$ is finite for all simple polygons if and only if $p\in (0,3)$. For the intermediate energies $\mathcal{I}_{p}$ and $\mathcal{U}_{p}$ we obtain the analogous result for $p\in (0,2)$ and $p\in (0,1)$, respectively.

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Sebastian Scholtes. 2012-02-02. For which positive $p$ is the integral Menger curvature $\mathcal{M}_{p}$ finite for all simple polygons?. https://arxiv.org/abs/1202.0504

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