Fourier restriction, polynomial curves and a geometric inequality

We announce a Fourier restriction result for general polynomial curves in Click to view the MathML source. 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.