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