Fourier restriction, polynomial curves and a geometric inequality

We announce a Fourier restriction result for general polynomial curves in R^d. Measuring the Fourier restriction with respect to the affine arclength measure of the curve, we obtain a universal bound for the class of all polynomial curves of bounded degree. Our method relies on establishing a geometric inequality for general polynomial curves which is of interest in its own right. There are applications of this geometric inequality to other problems in euclidean harmonic analysis. To cite this article: S. Dendrinos, J. Wright, C. R. Acad. Sci. Paris, Ser. I 346 (2008).