Vertex Classification of Planar C-polygons

Illya Ivanov; Cameron Strachan

doi:10.1007/s00022-024-00734-5

paper

Vertex Classification of Planar C-polygons

arXiv:2211.16621 · doi:10.1007/s00022-024-00734-5

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 $n + m$ .