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arXiv · 1705.05019

Semiclassical measures on hyperbolic surfaces have full support

Semyon Dyatlov·Long Jin
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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].

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Semyon Dyatlov, Long Jin. 2017-05-14. Semiclassical measures on hyperbolic surfaces have full support. https://doi.org/10.4310/acta.2018.v220.n2.a3

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