Multilinear eigenfunction estimates for the Laplace spectral projectors on compact manifolds

TL;DR

This paper extends bilinear eigenfunction estimates for the Laplace operator from 2D to higher dimensions on compact manifolds and introduces related trilinear estimates.

Contribution

It generalizes previous bilinear eigenfunction estimates to all space dimensions and provides new trilinear estimates for Laplace eigenfunctions.

Findings

Extended bilinear estimates to higher dimensions

Derived new trilinear eigenfunction estimates

Applicable to compact manifolds without boundary

Abstract

The purpose of this note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained in a previous work in dimension 2. We also give some related trilinear estimates.