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RESEARCH PRODUCT
On the Dimension of Kakeya Sets in the First Heisenberg Group
Jiayin Liusubject
Mathematics - Metric GeometryMathematics - Classical Analysis and ODEsApplied MathematicsGeneral MathematicsMathematics::Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsfraktaalitCondensed Matter::Strongly Correlated ElectronsMetric Geometry (math.MG)mittateoriaPrimary 28A75 Secondary 28A78 28A80description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-06-22 |