On the Dimension of Kakeya Sets in the First Heisenberg Group
arXiv:2106.11937
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 -plane is a Kakeya set with Heisenberg Hausdorff dimension 3.
11 pages, 3 figures