April 30, 2024Open Access

Bi-Lipschitz rigidity of discrete subgroups

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Resumen

We obtain a bi-Lipschitz rigidity theorem for a Zariski dense discrete subgroup of a connected simple real algebraic group. As an application, we show that any Zariski dense discrete subgroup of a higher rank semisimple algebraic group G cannot have a C¹-smooth antipodal limit set in G/P for any non-maximal parabolic subgroup P.

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Cite This Study

Canary et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6cdf2b6db64358764be9c https://doi.org/https://doi.org/10.48550/arxiv.2405.00249

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1Zariski Dense Subgroups of Semisimple Algebraic Groups with Isomorphic p-adic Closures2003
2Rigidity of Kleinian groups via self‐joinings: measure theoretic criterion2025
3Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spaces2025
4A connection between Lipschitz and Kazhdan constants for groups of homeomorphisms of the real line2026
5Remarks on discrete subgroups with full limit sets in higher rank Lie groups2024

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