Decoupling for two quadratic forms in three variables: a complete characterization

TL;DR

This paper establishes precise decoupling inequalities for degenerate surfaces defined by pairs of quadratic forms in three variables, completing the classification of such inequalities in this setting.

Contribution

It provides a complete characterization of decoupling inequalities for all degenerate surfaces of codimension two in five-dimensional space, extending previous non-degenerate results.

Findings

Sharp decoupling inequalities for degenerate surfaces

Complete classification of decoupling inequalities for pairs of quadratic forms

Extension of previous non-degenerate case results

Abstract

We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in $\mathbb{R}^5$ given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case (arXiv:1609.04107), this provides a classification of decoupling inequalities for pairs of quadratic forms in three variables.