Nonexistence of extremizers for certain convex curves

Abstract

We establish the nonexistence of extremizers for a local Fourier restriction inequality on a certain class of planar convex curves whose curvature satisfies a natural assumption. We accomplish this by studying the local behavior of the triple convolution of the arclength measure on the curve with itself, and show in particular that every extremizing sequence concentrates at a point on the curve.

11 pages

References in corpus (2)

• Existence of Extremals for a Fourier Restriction Inequality
• On the extremizers of an adjoint Fourier restriction inequality

Cited by in corpus (1)

• Some recent progress on sharp Fourier restriction theory