Fractal Weyl laws for asymptotically hyperbolic manifolds
Author(s)
Datchev, Kiril; Dyatlov, Semyon
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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.
Date issued
2013-04Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1016-443X
1420-8970