English

Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions

Analysis of PDEs 2016-01-20 v1 Classical Analysis and ODEs Differential Geometry

Abstract

We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.

Keywords

Cite

@article{arxiv.1409.1286,
  title  = {Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions},
  author = {Matthew D. Blair and Christopher D. Sogge},
  journal= {arXiv preprint arXiv:1409.1286},
  year   = {2016}
}

Comments

17 pages, 2 figures

R2 v1 2026-06-22T05:48:09.111Z