Local Mixing and Invariant Measures for Horospherical Subgroups on Abelian Covers
2018 ◽
Vol 2019
(19)
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pp. 6036-6088
Keyword(s):
Rank One
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Abstract Abelian covers of hyperbolic three-manifolds are ubiquitous. We prove the local mixing theorem of the frame flow for abelian covers of closed hyperbolic three-manifolds. We obtain a classification theorem for measures invariant under the horospherical subgroup. We also describe applications to the prime geodesic theorem as well as to other counting and equidistribution problems. Our results are proved for any abelian cover of a homogeneous space Γ0∖G where G is a rank one simple Lie group and Γ0 < G is a convex cocompact Zariski dense subgroup.
2012 ◽
Vol 148
(4)
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pp. 1051-1084
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Keyword(s):
2015 ◽
Vol 210
(1)
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pp. 467-507
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2001 ◽
Vol 21
(1)
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pp. 93-114
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1998 ◽
Vol 18
(2)
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pp. 503-507
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Keyword(s):
2009 ◽
Vol 30
(1)
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pp. 131-150
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Keyword(s):
2021 ◽
Vol 25
(24)
◽
pp. 732-747
2009 ◽
Vol 29
(5)
◽
pp. 1417-1449
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Keyword(s):