Harmonic and invariant measures on foliated spaces
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- by Chris Connell and Matilde Martínez PDF
- Trans. Amer. Math. Soc. 369 (2017), 4931-4951 Request permission
Abstract:
We consider the family of harmonic measures on a lamination $\mathscr {L}$ of a compact space $X$ by locally symmetric spaces $L$ of noncompact type, i.e. $L\cong \Gamma _L\backslash G/K$. We establish a natural bijection between these measures and the measures on an associated lamination foliated by $G$-orbits, $\widehat {\mathscr {L}}$, which are right invariant under a minimal parabolic (Borel) subgroup $B<G$. In the special case when $G$ is split, these measures correspond to the measures that are invariant under both the Weyl chamber flow and the stable horospherical flows on a certain bundle over the associated Weyl chamber lamination. We also show that the measures on $\widehat {\mathscr {L}}$ right invariant under two distinct minimal parabolics, and therefore all of $G$, are in bijective correspondence with the holonomy invariant ones.References
Additional Information
- Chris Connell
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 666258
- Matilde Martínez
- Affiliation: Department of Mathematics, Universidad de la República, 2544 Montevideo, Uruguay
- MR Author ID: 788590
- Received by editor(s): December 15, 2009
- Received by editor(s) in revised form: October 29, 2012, and August 15, 2015
- Published electronically: March 6, 2017
- Additional Notes: The first author was supported by NSF grant DMS-0608643
The second author was supported by ANII, research grant FCE2007 106. - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4931-4951
- MSC (2010): Primary 37C40, 53C12, 58J65; Secondary 57R30, 37D40
- DOI: https://doi.org/10.1090/tran/6811
- MathSciNet review: 3632555