Semiclassical measures on hyperbolic surfaces have full support

Semyon Dyatlov University of California, Berkeley and Massachusetts Institute of Technology Long Jin Yau Mathematical Science Center, Tsinghua University

Analysis of PDEs Dynamical Systems mathscidoc:1808.03001

Acta Mathematica
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 by Dyatlov-Zahl and proved for porous sets in Bourgain-Dyatlov.
Quantum chaos, semiclassical measure, hyperbolic surfaces
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@inproceedings{semyonsemiclassical,
  title={Semiclassical measures on hyperbolic surfaces have full support},
  author={Semyon Dyatlov, and Long Jin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180806160233266816128},
  booktitle={Acta Mathematica},
}
Semyon Dyatlov, and Long Jin. Semiclassical measures on hyperbolic surfaces have full support. In Acta Mathematica. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180806160233266816128.
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