Semiclassical measures on hyperbolic surfaces have full support
Name
1705.05019.pdf
Description
Accepted version
Size
676.31 KB
Format
Adobe PDF
Checksum (MD5)
156cd55d9439cf52a88328f777f34644
Author(s)
Dyatlov, Semen
Jin, Long
Date Issued
August 2018
Journal
Acta Mathematica
Publisher
International Press of Boston
Citation
Dyatlov, Semyon, and Long Jin. "Semiclassical measures on hyperbolic surfaces have full support." Acta Mathematica, 220, 2 (2018): 297–339 © 2018 International Press of Boston
Version
Author's final manuscript
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 “Spectral gaps, additive energy, and a fractal uncertainty principle” [Dyatlov, S. & Zahl, J. Geom. Funct. Anal., 26 (2016), 1011–1094] and proved for porous sets in “Spectral gaps without the pressure condition” [Bourgain, J. & Dyatlov, S. Ann. of Math., 187 (2018), 825–867].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4310/acta.2018.v220.n2.a3
