Diagonal Fourier restriction for positively curved surfaces in R³
Follow the latest progress by email.
For a compact smooth positively curved surface Σ⊂R³, possibly with smooth boundary, does the Fourier extension operator map Lᵖ(Σ) into Lᵖ(R³) for every 3<p<∞?
Why it matters and what counts as progress
Why it matters: The diagonal p>3 range is a sharp general-surface restriction target in three-dimensional Fourier analysis.
What counts as progress: Reach the full diagonal p>3 range or prove sharper endpoint and quantitative estimates for specified surface classes.
How the problem developed
- 1979 · Theorem [1]
Elias M. Stein and Peter A. Tomas Established the classical L²-to-L⁴ restriction estimate for positively curved surfaces, a foundational non-diagonal result.
- 2024 · Partial result [1]
Shukun Wang and Ruixiang Wu Proved the diagonal estimate in the cited range p>22/7, improving earlier bounds while leaving the interval down to p>3 open.
- 24 Sept 2026 · Reported claim [1]
OpenAI The manuscript claims the diagonal L^p surface-to-volume estimate for every p>3 on compact smooth positively curved surfaces, including smooth boundary.
AI contribution
Diagonal Fourier extension for positively curved surfaces in three dimensions
For every compact smooth positively curved surface Σ in R³, including smooth boundary, and every 3<p<∞, the Fourier extension operator maps Lᵖ(Σ) to Lᵖ(R³).
Sources
Website timeline
Publication dates and editorial changes.
OpenAI reports diagonal Fourier restriction for positively curved surfaces