Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 077-02. Diagonal Fourier extension for positively curved surfaces in three dimensions
Manuscript map · lines 4005–4014
OpenAI@2026-10-07#rem:oai-p-077-02
Authors: OpenAI. Family 077.
Title: Diagonal Fourier extension for positively curved surfaces in three dimensions.
Abstract: We prove the diagonal Fourier extension conjecture for compact smooth positively curved surfaces ${}Sigma{}subset{}mathbb R{}3$, including surfaces with smooth boundary. For every $3{}lt p{}lt {}infty$, the extension operator maps $L{}p({}Sigma)$ boundedly into $L{}p({}mathbb R{}3)$. The compact paraboloid case also yields free Schrödinger local smoothing in two spatial dimensions for every $3{}lt p{}lt {}infty$ and Sobolev order $s{}gt 2-6/p$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros