ON THE DIMENSION OF KAKEYA SETS IN THE FIRST HEISENBERG GROUP

ON THE DIMENSION OF KAKEYA SETS IN THE FIRST HEISENBERG GROUP

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. © 2022 American Ma...

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Bibliographic Details
Main Author: Liu, J. (Author)
Format: Article
Language:English
Published: American Mathematical Society 2022
Subjects:
Hausdorff dimension
Heisenberg group
Kakeya set
Online Access:View Fulltext in Publisher
LEADER 00881nam a2200169Ia 4500
001 10.1090-proc-15914
008 220706s2022 CNT 000 0 und d
020 |a 00029939 (ISSN) 
245 1 0 |a ON THE DIMENSION OF KAKEYA SETS IN THE FIRST HEISENBERG GROUP 
260 0 |b American Mathematical Society  |c 2022 
856 |z View Fulltext in Publisher  |u https://doi.org/10.1090/proc/15914 
520 3 |a 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. © 2022 American Mathematical Society. 
650 0 4 |a Hausdorff dimension 
650 0 4 |a Heisenberg group 
650 0 4 |a Kakeya set 
700 1 |a Liu, J.  |e author 
773 |t Proceedings of the American Mathematical Society 

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