Mathematics > Metric Geometry
arXiv:2509.05711 (math)
[Submitted on 6 Sep 2025 (v1), last revised 29 May 2026 (this version, v2)]
Abstract:In 1971, Cunningham proved that every star-shaped Kakeya set $E\subset\mathbb{R}^2$ satisfies $|E| \geq \pi/108$. In this paper, we show that Cunningham's bound is not optimal and can be improved to $|E| \geq \pi/98$.
Submission history
From: Shaoqi Li [view email]
[v1]
Sat, 6 Sep 2025 13:19:02 UTC (39 KB)
[v2]
Fri, 29 May 2026 15:22:11 UTC (41 KB)
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