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arXiv · 1909.00852

Disks in Curves of Bounded Convex Curvature

Anders Aamand·Mikkel Abrahamsen·Mikkel Thorup
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Abstract

We say that a simple, closed curve $\gamma$ in the plane has bounded convex curvature if for every point $x$ on $\gamma$, there is an open unit disk $U_x$ and $\varepsilon_x>0$ such that $x\in\partial U_x$ and $B_{\varepsilon_x}(x)\cap U_x\subset\text{Int}\;\gamma$. We prove that the interior of every curve of bounded convex curvature contains an open unit disk.

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Anders Aamand, Mikkel Abrahamsen, Mikkel Thorup. 2019-09-02. Disks in Curves of Bounded Convex Curvature. https://arxiv.org/abs/1909.00852

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