Diagonal Fourier extension for positively curved surfaces in three dimensions
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 $s\gt 2-6/p$.
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions
curl -X POST /api/v1/records/openai-math/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Diagonal-Fourier-extension-for-positively-curved-surfaces-in-three-dimensions/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'