What does this research mean for the field?

The Fourier restriction conjecture for the sphere in three-dimensional Euclidean space is true, proven by establishing a four-dimensional one-parameter Riemannian dynamic metric deformation system. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish the L^p–L^q boundedness of the spherical Fourier extension operator and completely prove the Fourier restriction conjecture for the sphere in three-dimensional Euclidean space.

September 8, 2026Open Access

Complete Proof of the Fourier Restriction Conjecture via a Four-Dimensional Riemannian Deformation Geometry Framework

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Authors

CWChangmin Wei

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Implication

Mathematical analysis demonstrates complete proof of the spherical Fourier restriction conjecture in three dimensions, resolving a long-standing open problem in harmonic analysis.

Key Points

To establish the L^p–L^q boundedness of the spherical Fourier extension operator and completely prove the Fourier restriction conjecture for the sphere in three-dimensional Euclidean space.
Constructed a four-dimensional one-parameter Riemannian dynamic metric deformation system featuring a smooth traceless deformation family from ellipsoidal metrics to the spherically symmetric metric.
Integrated uniform bi-Lipschitz geometric transfer, curvature-induced phase dissipation, four-dimensional Kakeya incidence counting invariance, and hyperplane section dimensional reduction interpolation.
Implemented a Lean 4 formal verification skeleton to enable computer-assisted verification of the mathematical conclusions.
Successfully eliminated classical endpoint obstructions and high-frequency wave packet coherent resonance through metric deformation.
Established the complete mathematical proof confirming that the Fourier restriction conjecture holds for the sphere in three-dimensional Euclidean space.

Cite This Study

Changmin Wei (2026) studied this question.

synapsesocial.com/papers/6a9fd82f58e84d0ff5b47743 https://doi.org/10.5281/zenodo.22639164

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Implication

Mathematical analysis demonstrates complete proof of the spherical Fourier restriction conjecture in three dimensions, resolving a long-standing open problem in harmonic analysis.

Complete Proof of the Fourier Restriction Conjecture via a Four-Dimensional Riemannian Deformation Geometry Framework

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Implication

Key Points

Cite This Study

Complete Proof of the Fourier Restriction Conjecture via a Four-Dimensional Riemannian Deformation Geometry Framework

Discussion

Member takes

Implication

Key Points

Cite This Study

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