An improved lower bound for star-shaped Kakeya sets

Abstract

In 1971, Cunningham proved that every star-shaped Kakeya set $E\subset {\mathbb{R}}^2$ satisfies $|E|\ge \ddot{I}€/108$. In this paper, we show that Cunningham's bound is not optimal and can be improved to $|E|\ge \ddot{I}€/98$.

16 pages, 7 figures, the final version of the article is published in Ann. Fenn. Math