Resumen de Fourier restriction to convex surfaces of revolution in R3

F. Abi-Khuzam, Bassam Shayya

• If U is a c~ hypersurface in lito and da is induced Leheogne msasure 00 E, then it is well known that a Tomas-Stein Fourier restrirtion estimate 00 1? implies that E has a nowhere vanishing Gaussian curvature. lo a recení paper, Carhery and Ziesler ohuerved thaI if induced Leheogne measure is replaced hy afflne surface area, then a Tomas-Sísin restriction estimate 00 1 implies that E satisfies the afflne isoperimetrir inequality. Since the only property needed for a h'ypersurface tu satisfy the affine isoperimetrir inequality is convexity, this raised the question of whether a Tomas Stein restriction estimate can he ohtained for fiat hut convex hypersurfaces in J5~ such as E(s) - (x, c1/' 1 ) m - 1 2 .... We prove that this is indeed the case in dimension u - 3.