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arXiv · 2204.00206

Isometric group actions with vanishing rate of escape on CAT(0) spaces

Hiroyasu Izeki
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Abstract

Let $Γ$ be a finitely generated group equipped with a symmetric and nondegenerate probability measure $μ$ with finite second moment, and $Y$ a CAT(0) space which is either proper or of finite telescopic dimension. We show that if an isometric action of $Γ$ on $Y$ has vanishing rate of escape with respect to $μ$ and does not fix a point in the boundary at infinity of $Y$, then there exists a flat subspace in $Y$ which is left invariant under the action of $Γ$. In the proof of this result, an equivariant $μ$-harmonic map from $Γ$ into $Y$ plays an important role.

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BibTeXRIS

Hiroyasu Izeki. 2022-10-30. Isometric group actions with vanishing rate of escape on CAT(0) spaces. https://doi.org/10.1007/s00039-023-00628-9

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