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Semiclassical measures on hyperbolic surfaces have full support
Acta Mathematica ( IF 3.7 ) Pub Date : 2018-01-01 , DOI: 10.4310/acta.2018.v220.n2.a3
Semyon Dyatlov 1 , Long Jin 2
Affiliation  

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].

中文翻译:

双曲曲面上的半经典测度有充分的支持

我们表明,从拉普拉斯算子在紧凑双曲线表面上的一系列特征函数获得的每个限制半经典测度都支持整个共球丛。证明的关键新要素是分形不确定性原理,首先在 [arXiv:1504.06589] 中提出,并在 [arXiv:1612.09040] 中证明了多孔集。
更新日期:2018-01-01
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