An improved lower bound for star-shaped Kakeya sets

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