Fractal Weyl laws for asymptotically hyperbolic manifolds
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 co...
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| Format: | Article |
| Language: | English |
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Springer Basel
2016
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| Online Access: | http://hdl.handle.net/1721.1/104012 |
| _version_ | 1826188161758265344 |
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| author | Datchev, Kiril Dyatlov, Semyon |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Datchev, Kiril Dyatlov, Semyon |
| author_sort | Datchev, Kiril |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T07:55:30Z |
| format | Article |
| id | mit-1721.1/104012 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T07:55:30Z |
| publishDate | 2016 |
| publisher | Springer Basel |
| record_format | dspace |
| spelling | mit-1721.1/1040122022-09-23T09:41:26Z Fractal Weyl laws for asymptotically hyperbolic manifolds Datchev, Kiril Dyatlov, Semyon Massachusetts Institute of Technology. Department of Mathematics Datchev, Kiril 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. National Science Foundation (U.S.) (NSF postdoctoral research fellowship) National Science Foundation (U.S.) (NSF grant DMS-1201417) 2016-08-26T14:21:23Z 2016-08-26T14:21:23Z 2013-04 2012-12 2016-08-18T15:40:19Z Article http://purl.org/eprint/type/JournalArticle 1016-443X 1420-8970 http://hdl.handle.net/1721.1/104012 Datchev, Kiril, and Semyon Dyatlov. “Fractal Weyl Laws for Asymptotically Hyperbolic Manifolds.” Geometric and Functional Analysis 23, no. 4 (April 7, 2013): 1145–1206. en http://dx.doi.org/10.1007/s00039-013-0225-8 Geometric and Functional Analysis 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. Springer Basel application/pdf Springer Basel Springer Basel |
| spellingShingle | Datchev, Kiril Dyatlov, Semyon Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title | Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title_full | Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title_fullStr | Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title_full_unstemmed | Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title_short | Fractal Weyl laws for asymptotically hyperbolic manifolds |
| title_sort | fractal weyl laws for asymptotically hyperbolic manifolds |
| url | http://hdl.handle.net/1721.1/104012 |
| work_keys_str_mv | AT datchevkiril fractalweyllawsforasymptoticallyhyperbolicmanifolds AT dyatlovsemyon fractalweyllawsforasymptoticallyhyperbolicmanifolds |