Spectral gaps, additive energy, and a fractal uncertainty principle
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39_2016_378_ReferencePDF.pdf
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1.41 MB
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Checksum (MD5)
745ab522bbe24c2000ae767066c4a0f0
Author(s)
Dyatlov, Semen
Zahl, Joshua
Date Issued
August 2016
Journal
Geometric and Functional Analysis
Publisher
Springer International Publishing
Citation
Dyatlov, Semyon, and Joshua Zahl. “Spectral Gaps, Additive Energy, and a Fractal Uncertainty Principle.” Geometric and Functional Analysis 26.4 (2016): 1011–1094.
Version
Author's final manuscript
Abstract
We obtain an essential spectral gap for n-dimensional convex co-compact hyperbolic manifolds with the dimension δ 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00039-016-0378-3
