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

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.

v2: 19 pages, small corrections following referee report

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• On integer solutions of Parsell-Vinogradov systems
• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• Decoupling for certain quadratic surfaces of low co-dimensions
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Cited by in corpus (4)

• Decoupling inequalities for quadratic forms
• Supercritical discrete restriction estimates for forms in many variables
• Fourier decay of fractal measures on surfaces of co-dimension two in ${\mathbb{R}}^5$
• Fourier restriction estimates for surfaces of co-dimension two in ${\mathbb{R}}^5$