Semiclassical measures on hyperbolic surfaces have full support

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].

39 pages, 3 figures; changed following the referees' suggestions. To appear in Acta Math

References in corpus (1)

• Damped wave equations on compact hyperbolic surfaces

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