Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two   dimensions
  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. 
Matthew D. Blair and Christopher D. Sogge
math.AP math.CA math.DG