On the Dimension of Kakeya Sets in the First Heisenberg Group

2021/06/22 by Jiayin Liu, Liu, Jiayin · 2 citations
Mathematics · #28A80 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #Primary 28A75 #Secondary 28A78

paper · pdf · doi:10.48550/arxiv.2106.11937

openalex publication_date 2021/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define Kakeya sets in the Heisenberg group and show that the Heisenberg Hausdorff dimension of Kakeya sets in the first Heisenberg group is at least 3. This lower bound is sharp since, under our definition, the \xoy\-plane is a Kakeya set with Heisenberg Hausdorff dimension 3.

Cited by

• On the Dimension of the CC-geodesic Kakeya sets in the first Heisenberg group
• An L^4/3 SL₂ Kakeya maximal inequality

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