Semiclassical measures on hyperbolic surfaces have full support
Analysis of PDEs
2018-08-17 v3 Spectral Theory
Chaotic Dynamics
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].
Cite
@article{arxiv.1705.05019,
title = {Semiclassical measures on hyperbolic surfaces have full support},
author = {Semyon Dyatlov and Long Jin},
journal= {arXiv preprint arXiv:1705.05019},
year = {2018}
}
Comments
39 pages, 3 figures; changed following the referees' suggestions. To appear in Acta Math