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- Publisher Website: 10.1112/S0010437X19007139
- Scopus: eid_2-s2.0-85080869231
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Article: Local-global principles in circle packings
Title | Local-global principles in circle packings |
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Authors | |
Keywords | local-to-global Kleinian group circle method Apollonian circle packing |
Issue Date | 2019 |
Publisher | Foundation Compositio Mathematica. The Journal's web site is located at https://compositio.nl/compositio.html |
Citation | Compositio Mathematica, 2019, v. 155 n. 6, p. 1118-1170 How to Cite? |
Abstract | We generalize work by Bourgain and Kontorovich [On the local-global conjecture for integral Apollonian gaskets, Invent. Math. 196 (2014), 589–650] and Zhang [On the local-global principle for integral Apollonian 3-circle packings, J. Reine Angew. Math. 737, (2018), 71–110], proving an almost local-to-global property for the curvatures of certain circle packings, to a large class of Kleinian groups. Specifically, we associate in a natural way an infinite family of integral packings of circles to any Kleinian group A⩽PSL2(K) satisfying certain conditions, where K is an imaginary quadratic field, and show that the curvatures of the circles in any such packing satisfy an almost local-to-global principle. A key ingredient in the proof is that A possesses a spectral gap property, which we prove for any infinite-covolume, geometrically finite, Zariski dense Kleinian group in PSL2(OK) containing a Zariski dense subgroup of PSL2(Z) . |
Persistent Identifier | http://hdl.handle.net/10722/289728 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 2.490 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Fuchs, E | - |
dc.contributor.author | Stange, KE | - |
dc.contributor.author | Zhang, X | - |
dc.date.accessioned | 2020-10-22T08:16:37Z | - |
dc.date.available | 2020-10-22T08:16:37Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Compositio Mathematica, 2019, v. 155 n. 6, p. 1118-1170 | - |
dc.identifier.issn | 0010-437X | - |
dc.identifier.uri | http://hdl.handle.net/10722/289728 | - |
dc.description.abstract | We generalize work by Bourgain and Kontorovich [On the local-global conjecture for integral Apollonian gaskets, Invent. Math. 196 (2014), 589–650] and Zhang [On the local-global principle for integral Apollonian 3-circle packings, J. Reine Angew. Math. 737, (2018), 71–110], proving an almost local-to-global property for the curvatures of certain circle packings, to a large class of Kleinian groups. Specifically, we associate in a natural way an infinite family of integral packings of circles to any Kleinian group A⩽PSL2(K) satisfying certain conditions, where K is an imaginary quadratic field, and show that the curvatures of the circles in any such packing satisfy an almost local-to-global principle. A key ingredient in the proof is that A possesses a spectral gap property, which we prove for any infinite-covolume, geometrically finite, Zariski dense Kleinian group in PSL2(OK) containing a Zariski dense subgroup of PSL2(Z) . | - |
dc.language | eng | - |
dc.publisher | Foundation Compositio Mathematica. The Journal's web site is located at https://compositio.nl/compositio.html | - |
dc.relation.ispartof | Compositio Mathematica | - |
dc.rights | Compositio Mathematica. Copyright © Foundation Compositio Mathematica. | - |
dc.subject | local-to-global | - |
dc.subject | Kleinian group | - |
dc.subject | circle method | - |
dc.subject | Apollonian circle packing | - |
dc.title | Local-global principles in circle packings | - |
dc.type | Article | - |
dc.identifier.email | Zhang, X: xz27@hku.hk | - |
dc.identifier.authority | Zhang, X=rp02608 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1112/S0010437X19007139 | - |
dc.identifier.scopus | eid_2-s2.0-85080869231 | - |
dc.identifier.hkuros | 317202 | - |
dc.identifier.volume | 155 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 1118 | - |
dc.identifier.epage | 1170 | - |
dc.identifier.isi | WOS:000471309900003 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0010-437X | - |