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

We prove bilinear ${\mathrm{\ell }}^2$-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 $p>22\mathrm{/}7$, matching an earlier result for the elliptic paraboloid.