Lp Bilinear Quasimode Estimates

Zihua Guo, Xiaolong Han, Melissa Tacy

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In this paper, we investigate the Lp 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 Lp bilinear eigenfunction estimates. We further show that all of these estimates are sharp by constructing various quasimodes and eigenfunctions that saturate our estimates.

Original languageEnglish
Pages (from-to)2242-2289
Number of pages48
JournalJournal of Geometric Analysis
Issue number3
Publication statusPublished - Jul 2019


  • Bilinear estimates
  • Eigenfunctions
  • Laplacian
  • Quasimodes

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