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PreprintCC BY-NC-SA 4.0arXiv

Kakeya and Furstenberg problems for sticky sets of tubes

  • Hong Wang
  • Dmitrii Zakharov
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Abstract

We study incidence problems for sticky sets of tubes. In the first part, we prove a sharp Furstenberg set estimate for sticky sets of tubes in ℝ3 satisfying convex Wolff axioms. In the second part, we prove the Kakeya set conjecture in ℝ4 for sticky sets of tubes satisfying convex Wolff axioms.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026kakeya,
  title = {{Kakeya and Furstenberg problems for sticky sets of tubes}},
  author = {Hong Wang and Dmitrii Zakharov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22035},
  eprint = {2609.22035},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22035},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Kakeya and Furstenberg problems for sticky sets of tubes
AU  - Hong Wang
AU  - Dmitrii Zakharov
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22035
UR  - https://arxiv.org/abs/2609.22035
AB  - We study incidence problems for sticky sets of tubes. In the first part, we prove a sharp Furstenberg set estimate for sticky sets of tubes in ℝ^3 satisfying convex Wolff axioms. In the second part, we prove the Kakeya set conjecture in ℝ^4 for sticky sets of tubes satisfying convex Wolff axioms.
ER  -