Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
arXiv:1409.1286 · doi:10.2140/apde.2015.8.747
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.
17 pages, 2 figures