An improved lower bound for star-shaped Kakeya sets

Authors

  • Shaoqi Li Sun Yat-sen University, Department of Mathematics

DOI:

https://doi.org/10.54330/afm.185132

Keywords:

Kakeya set, star-shaped, lower bound

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 \(|E| \geq \pi/98\).

 

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Published

2026-05-29

Issue

Vol. 51 No. 1 (2026)

Section

Articles

License

Copyright (c) 2026 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Li, S. (2026). An improved lower bound for star-shaped Kakeya sets. Annales Fennici Mathematici, 51(1), 377–392. https://doi.org/10.54330/afm.185132