Fractal Weyl laws for asymptotically hyperbolic manifolds
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Author(s)
Datchev, Kiril
Dyatlov, Semyon
Date Issued
April 2013
Journal
Geometric and Functional Analysis
Publisher
Springer Basel
Citation
Datchev, Kiril, and Semyon Dyatlov. “Fractal Weyl Laws for Asymptotically Hyperbolic Manifolds.” Geometric and Functional Analysis 23, no. 4 (April 7, 2013): 1145–1206.
Version
Author's final manuscript
Abstract
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined by the dimension of the trapped set. This covers the case of general convex cocompact quotients (including the case of connected trapped sets) where our result implies a bound on the number of zeros of the Selberg zeta function in disks of arbitrary size along the imaginary axis. Although no sharp fractal lower bounds are known, the case of quasifuchsian groups, included here, is most likely to provide them.
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/s00039-013-0225-8
