What does this research mean for the field?

The Kakeya maximal conjecture holds in Euclidean space for all dimensions n ≥ 4, establishing that any Kakeya set has a Hausdorff dimension equal to the ambient dimension. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To resolve the high-dimensional Kakeya maximal conjecture for dimensions n ≥ 4, determining whether any compact set containing a unit line segment in every direction must have full Hausdorff dimension n.

September 8, 2026Open Access

Proof of the High-Dimensional Kakeya Maximal Conjecture (n ≥ 4) Based on the UTE General Transport Equation Framework

View Full Paper

Ask AI

Bookmark

Authors

CWChangmin Wei

Discussion

Member takes

Implication

Mathematical analysis demonstrates the validity of the Kakeya maximal conjecture in dimensions four and higher, indicating major advances for harmonic analysis and wave propagation models.

Key Points

To resolve the high-dimensional Kakeya maximal conjecture for dimensions n ≥ 4, determining whether any compact set containing a unit line segment in every direction must have full Hausdorff dimension n.
Constructed a Universal Transport Equation Riemannian metric deformation flow evolving ellipsoidal configurations into spherically symmetric geometry.
Established uniform bi-Lipschitz geometric transfer, Hausdorff dimension invariance, and curvature-induced phase dissipation to preserve the incidence integral.
Integrated Fubini-type projection section estimates and embedded a Lean 4 formal verification skeleton to ensure rigorous proof logic.
Proved the finiteness, positivity, and conservation of the incidence integral during metric deformation to close the contradiction chain.
Established that the Kakeya maximal conjecture holds without additional assumptions in Euclidean space for all dimensions n ≥ 4, confirming full Hausdorff dimension.

Cite This Study

Changmin Wei (2026) studied this question.

synapsesocial.com/papers/6a9fd82f58e84d0ff5b478d3 https://doi.org/10.5281/zenodo.22641276

View Full Paper

Ask AI

Bookmark

Implication

Mathematical analysis demonstrates the validity of the Kakeya maximal conjecture in dimensions four and higher, indicating major advances for harmonic analysis and wave propagation models.

Proof of the High-Dimensional Kakeya Maximal Conjecture (n ≥ 4) Based on the UTE General Transport Equation Framework

Discussion

Member takes

Implication

Key Points

Cite This Study

Proof of the High-Dimensional Kakeya Maximal Conjecture (n ≥ 4) Based on the UTE General Transport Equation Framework

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider