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Title: Dichotomy and Measures on Limit Sets of Anosov Groups
Abstract Let $$G$$ be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup $$\Gamma <G$$, we show that a $$\Gamma $$-conformal measure is supported on the limit set of $$\Gamma $$ if and only if its dimension is $$\Gamma $$-critical. This implies the uniqueness of a $$\Gamma $$-conformal measure for each critical dimension, answering the question posed in our earlier paper with Edwards [13]. We obtain this by proving a higher rank analogue of the Hopf–Tsuji–Sullivan dichotomy for the maximal diagonal action. Other applications include an analogue of the Ahlfors measure conjecture for Anosov subgroups.  more » « less
Award ID(s):
1900101
PAR ID:
10519686
Author(s) / Creator(s):
;
Publisher / Repository:
Oxford Academic
Date Published:
Journal Name:
International Mathematics Research Notices
Volume:
2024
Issue:
7
ISSN:
1073-7928
Page Range / eLocation ID:
5658 to 5688
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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