Lp Bilinear Quasimode Estimates

Zihua Guo, Xiaolong Han, Melissa Tacy

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Abstract

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
Volume29
Issue number3
DOIs
Publication statusPublished - Jul 2019

Keywords

  • Bilinear estimates
  • Eigenfunctions
  • Laplacian
  • Quasimodes

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