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- W4308167029 abstract "A sublinear biLipschitz equivalence (SBE) between metric spaces is a map from one space to another that distorts distances with bounded multiplicative constants and sublinear additive error. Given any sublinear function $kappa$, $kappa$-Morse boundaries are defined for all geodesic proper metric spaces as a quasi-isometrically invariant and metrizable topological space of quasi-geodesic rays. In this paper, we prove that $kappa$-Morse boundaries of proper geodesic metric spaces are invariant under suitable SBEs. A tool in the proof is the use of sublinear rays, that is, sublinear bilispchitz embeddings of the half line, generalizing quasi-geodesic rays. As an application we distinguish a pair of right-angled Coxeter groups brought up by Behrstock up to sublinear biLipschitz equivalence. We also show that under mild assumptions, generic random walks on countable groups are sublinear rays." @default.
- W4308167029 created "2022-11-08" @default.
- W4308167029 creator A5039097660 @default.
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- W4308167029 date "2022-11-02" @default.
- W4308167029 modified "2023-10-17" @default.
- W4308167029 title "Sublinear biLipschitz equivalence and sublinearly Morse boundaries" @default.
- W4308167029 doi "https://doi.org/10.48550/arxiv.2211.01023" @default.
- W4308167029 hasPublicationYear "2022" @default.
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