On Radon Measures Invariant Under Horospherical Flows on Geometrically Infinite Quotients

Or Landesberg; Elon Lindenstrauss

doi:10.1093/imrn/rnab024

On Radon Measures Invariant Under Horospherical Flows on Geometrically Infinite Quotients

Or Landesberg^*
, Elon Lindenstrauss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider a locally finite (Radon) measure on SO+ (d, 1)/ invariant under a horospherical subgroup of SO+ (d, 1) where is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not observe any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable f low (geodesic flow).

Original language	English
Pages (from-to)	11602-11641
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2022
Issue number	15
DOIs	https://doi.org/10.1093/imrn/rnab024
State	Published - 1 Jul 2022

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© 2021 The Author(s) 2019. Published by Oxford University Press. All rights reserved.

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AB - We consider a locally finite (Radon) measure on SO+ (d, 1)/ invariant under a horospherical subgroup of SO+ (d, 1) where is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not observe any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable f low (geodesic flow).

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On Radon Measures Invariant Under Horospherical Flows on Geometrically Infinite Quotients

Abstract

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