Semiclassical measures on hyperbolic surfaces have full support
Author(s)Dyatlov, Semen; Jin, Long
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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].
DepartmentMassachusetts Institute of Technology. Department of Mathematics
International Press of Boston
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
Author's final manuscript