Download the PDF of the paper by Or Landesberg and Hee Oh titled “On the Density of Holospheres in Higher Order Homogeneous Spaces”

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overview: Let $ G $ be the connected semisimple real algebraic group and $\Gamma < G$ the Zariski dense discrete subgroup. Let $N$ be the maximal astrological subgroup of $G$, and $P=MAN$ be the minimal parabolic subgroup, the normalizer of $N$. Let $\mathcal{E}$ represent the unique $P$ minimal subset of $\Gamma \backslash G$ and let $\mathcal{E}_0$ be the $P^\circ$ minimal subset . Consider the notion of limit points of the astrological sphere at the F├╝rstenberg boundary $ G/P $ and show that for any $ the following are equivalent:[g]\in \mathcal{E}_0$: (1) $gP\in G/P$ is the limit point of the astrology. (2) $[g]NM$ is clustered inside $\mathcal{E}$. (3) $[g]N$ is clustered at $\mathcal{E}_0$. The equivalence of (1) and (2) is due to Darbo for the rank 1 case. We also observe that unlike the convex cocompact group of rank-1 Lie groups, $NM$ minimality of $\mathcal{E}$ does not hold in general Anosov homogeneous spaces.

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Birthplace: Ol Landesburg [view email]

[v1]

Thursday, February 10, 2022 13:59:35 UTC (17 KB)

[v2]

Thursday, May 25, 2023 17:56:30 UTC (17 KB)



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