TY - JOUR
T1 - On Radon Measures Invariant Under Horospherical Flows on Geometrically Infinite Quotients
AU - Landesberg, Or
AU - Lindenstrauss, Elon
N1 - Publisher Copyright:
© 2021 The Author(s) 2019. Published by Oxford University Press. All rights reserved.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - 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).
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).
UR - http://www.scopus.com/inward/record.url?scp=85135688795&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnab024
DO - 10.1093/imrn/rnab024
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AN - SCOPUS:85135688795
SN - 1073-7928
VL - 2022
SP - 11602
EP - 11641
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 15
ER -