Lp bilinear quasimode estimates

Abstract

In this paper, we investigate the $L^p$ bilinear quasimode estimates on compact Riemannian manifolds. We obtain results in the full range $p\ge 2$ on all $n$-dimensional manifolds with $n\ge 2$. This in particular implies the $L^p$ bilinear eigenfunction estimates. We further show that all of these estimates are sharp by constructing various quasimodes and eigenfunctions that saturate our estimates.

No change to major theorems or techniques. Final version

Cited by in corpus (1)

• A note on constructing sharp examples for $L^p$ norms of eigenfunctions and quasimodes near submanifolds