Uniform decoupling for convex curves

Abstract

Using a high/low argument, we prove a universal ${\ell }^2{L}^6$ decoupling estimate with constant $C_{\hat{I}}\mu R^{\hat{I}}\mu$ for general convex curves in the plane. These curves have no additional regularity assumptions, and the constant $C_{\hat{I}}\mu$ is uniform across all such curves.

52 pages. Comments are welcome