Uniform decoupling for convex curves

TL;DR

This paper proves a universal decoupling estimate for convex curves in the plane, applicable without regularity assumptions, with a constant uniform across all such curves, using a high/low argument.

Contribution

It introduces a universal $ ext{L}^6$ decoupling estimate for convex curves in the plane, independent of regularity assumptions, with a uniform constant.

Findings

Established a universal $ ext{L}^6$ decoupling estimate for convex curves

The estimate holds with a constant uniform across all convex curves

The proof employs a high/low argument technique

Abstract

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