Restriction inequalities for the hyperbolic hyperboloid

TL;DR

This paper develops new restriction inequalities for the hyperbolic hyperboloid in three dimensions, providing optimal results in certain bilinear ranges and advancing understanding in harmonic analysis.

Contribution

It introduces new unconditional and optimal restriction inequalities for the hyperbolic hyperboloid, expanding the theoretical framework in harmonic analysis.

Findings

Established unconditional restriction inequalities for q > 10/3

Provided optimal inequalities in the bilinear range

Enhanced understanding of restriction problems on hyperbolic surfaces

Abstract

In this article we establish new inequalities, both conditional and unconditional, for the restriction problem associated to the hyperbolic, or one-sheeted, hyperboloid in three dimensions, endowed with a Lorentz-invariant measure. These inequalities are unconditional (and optimal) in the bilinear range $q > \frac{10}{3}$.