Fourier restriction to convex surfaces of revolution in R3
Abi-Khuzam, Faruk
Shayya, Bassam
| Date: |
2006 |
| Abstract: |
If Γ is a C3 hypersurface in Rn and dσ is induced Lebesgue measure on Γ, then it is well known that a Tomas-Stein Fourier restriction estimate on Γ implies that Γ has a nowhere vanishing Gaussian curvature. In a recent paper, Carbery and Ziesler observed that if induced Lebesgue measure is replaced by affine surface area, then a Tomas-Stein restriction estimate on Γ implies that Γ satisfies the affine isoperimetric inequality. Since the only property needed for a hypersurface to satisfy the affine isoperimetric inequality is convexity, this raised the question of whether a TomasStein restriction estimate can be obtained for flat but convex hypersurfaces in Rn such as Γ(x) = (x, e−1/ $m ), m = 1, 2, . . . . We prove that this is indeed the case in dimension n = 3. |
| Rights: |
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| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Published in: |
Publicacions matemàtiques, V. 50 n. 1 (2006) p. 71-85, ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38264
DOI: 10.5565/PUBLMAT_50106_04
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Articles > Published articles > Publicacions matemàtiques
Articles > Research articles
Record created 2006-05-09, last modified 2024-12-02
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