Restriction and decoupling estimates for the hyperbolic paraboloid in $\mathbb{R}^3$

TL;DR

This paper establishes bilinear decoupling inequalities for the hyperbolic paraboloid in three dimensions and applies them to derive restriction estimates for p>22/7, aligning with known results for elliptic paraboloids.

Contribution

It introduces new bilinear decoupling inequalities for the hyperbolic paraboloid and applies these to obtain restriction estimates in a specific p-range.

Findings

Proved bilinear $ ext{ell}^2$-decoupling inequalities for the hyperbolic paraboloid.

Derived restriction estimates for p>22/7.

Matched earlier results for elliptic paraboloids.

Abstract

We prove bilinear $\ell^2$-decoupling and refined bilinear decoupling inequalities for the truncated hyperbolic paraboloid in $\mathbb{R}^3$. As an application, we prove the associated restriction estimate in the range $p>22/7$, matching an earlier result for the elliptic paraboloid.