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Mathematics > Spectral Theory
Title: Spectral gaps, additive energy, and a fractal uncertainty principle
(Submitted on 24 Apr 2015 (v1), last revised 11 May 2016 (this version, v3))
Abstract: We obtain an essential spectral gap for $n$-dimensional convex co-compact hyperbolic manifolds with the dimension $\delta$ of the limit set close to $(n-1)/2$. The size of the gap is expressed using the additive energy of stereographic projections of the limit set. This additive energy can in turn be estimated in terms of the constants in Ahlfors-David regularity of the limit set. Our proofs use new microlocal methods, in particular a notion of a fractal uncertainty principle.
Submission history
From: Semyon Dyatlov [view email][v1] Fri, 24 Apr 2015 18:23:50 GMT (207kb,D)
[v2] Fri, 14 Aug 2015 07:44:15 GMT (220kb,D)
[v3] Wed, 11 May 2016 13:58:55 GMT (674kb,D)
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