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Besicovitch's covering theorem in the parabolic metric
Abstract
We prove that Besicovitch's covering theorem holds for the parabolic metric dp((x1,t1),(x2,t2))=(|x1−x2|p+|t1−t2|p/2)1/p on ℝn×ℝ if and only if pgeqslant 2. If p=2, this answers a question posed by P. Mattila in the affirmative.
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BibTeX
@misc{dobronravov2026besicovitchs,
title = {{Besicovitch's covering theorem in the parabolic metric}},
author = {Nikita Dobronravov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15560},
eprint = {2609.15560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15560},
}
RIS
TY - UNPB
TI - Besicovitch's covering theorem in the parabolic metric
AU - Nikita Dobronravov
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15560
UR - https://arxiv.org/abs/2609.15560
AB - We prove that Besicovitch's covering theorem holds for the parabolic metric d_p((x_1,t_1),(x_2,t_2))=(|x_1−x_2|^p+|t_1−t_2|^p/2)^1/p on ℝ^n×ℝ if and only if pgeqslant 2. If p=2, this answers a question posed by P. Mattila in the affirmative.
ER -