{"id":"openai-math/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions","pdf":"https://github.com/openai/math/blob/main/preprints/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions-September-24-2026","tags":["harmonic-analysis","fourier-extension","geometric-analysis"],"score":0,"title":"Diagonal Fourier extension for positively curved surfaces in three dimensions","domain":"Real and complex analysis","family":"077","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"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 $`s\\gt 2-6/p`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Fourier restriction for positively curved surfaces"}