Diagonal Fourier extension for positively curved surfaces in three dimensions

OpenAI

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 for this record

What was already known

Wang and Wu had proved the diagonal estimate for p>22/7 on such surfaces; earlier bounds also had narrower exponent or input ranges.

AI involvement AI-led

OpenAI credits an internal model with the manuscripts. No individual interaction record establishes autonomous discovery.

OpenAI institutional authorship plus the released release’s internal-model production account supports model leadership, without an individual autonomy record.

Importance Major

Reaches the conjectured p>3 diagonal range for general positively curved surfaces in three dimensions.

Limitations

The separate bounded-data sphere theorem has an L∞ input and is only one input here. No completed human or machine check of the general-surface proof is documented.

Technical verification Reported

The manuscripts provide proofs and dependencies, but no completed human or machine check of the assessed general-surface theorem is documented.

Human understanding Few

No named person is documented as explaining the packet, density, and sparse-ball mechanism of the assessed result; this is a missing-evidence default.

Correction and publication history

2026-10-18 · publication

Reaches the conjectured p>3 diagonal range for general positively curved surfaces in three dimensions.

Read this published revision