L^p Bilinear Quasimode Estimates

In this paper, we investigate the L^p bilinear quasimode estimates on compact Riemannian manifolds. We obtain results in the full range p≥ 2 on all n-dimensional manifolds with n≥ 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.