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arXiv · 2211.16621

Vertex Classification of Planar C-polygons

Illya Ivanov·Cameron Strachan
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Abstract

Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$.

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Illya Ivanov, Cameron Strachan. 2022-11-29. Vertex Classification of Planar C-polygons. https://doi.org/10.1007/s00022-024-00734-5

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