arXiv:2106.11937 Abstract | arXiv Analytics

arXiv:2106.11937 [math.CA]Abstract References Reviews Resources

On the Dimension of Kakeya Sets in the First Heisenberg Group

Published 2021-06-22Version 1

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.

Comments: 11 pages, 3 figures

Categories: math.CA, math.MG

Subjects: 28A75, 28A78, 28A80

Keywords: first heisenberg group, heisenberg hausdorff dimension, define kakeya sets, lower bound, definition

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