An improved lower bound for star-shaped Kakeya sets

2025/09/06 by Li, Shaoqi
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2509.05711

Abstract

In 1971, Cunningham proved that every star-shaped Kakeya set E⊂ℝ² satisfies |E| ≥ π/108. In this paper, we show that Cunningham's bound is not optimal and can be improved to |E| ≥ π/98.

Citations

• Spectral Dimension Flow, Localized Non-Orientable Horizon Defects, and Emergent Time in Black Holes: A Geometry-Driven Effective Framework
• On Kakeya maps with regularity assumptions

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