Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao; Christopher D. Sogge; Yakun Xi; Jianwei Yang

doi:10.1016/j.jfa.2016.04.015

Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

Analysis of PDEs 2017-03-01 v2

Authors: Changxing Miao , Christopher D. Sogge , Yakun Xi , Jianwei Yang

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Abstract

We obtain an improvement of the bilinear estimates of Burq, G\'erard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by using microlocal techniques and a bilinear version of H\"ormander's oscillatory integral theorem.

Keywords

bilinear estimates Kakeya-Nikodym averages eigenfunctions compact Riemannian surfaces microlocal techniques oscillatory integral theorem

Cite

@article{arxiv.1602.06936,
  title  = {Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces},
  author = {Changxing Miao and Christopher D. Sogge and Yakun Xi and Jianwei Yang},
  journal= {arXiv preprint arXiv:1602.06936},
  year   = {2017}
}

Comments

19 pages, 1 figure. Affiliation corrected

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