Semiclassical measures on hyperbolic surfaces have full support (1705.05019v3)

Abstract: We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on the entire cosphere bundle. The key new ingredient for the proof is the fractal uncertainty principle, first formulated in [arXiv:1504.06589] and proved for porous sets in [arXiv:1612.09040].