Local $C^0$-semi-rigidity of meandering-hyperbolic actions

Sungwoon Kim

Local $C^0$-semi-rigidity of meandering-hyperbolic actions

Geometric Topology 2026-07-24 v1 Group Theory

Authors: Sungwoon Kim

Abstract

Meandering hyperbolicity, introduced by Kapovich, Kim, and Lee, extends classical hyperbolicity beyond the setting of word-hyperbolic groups. In this paper, we prove that every meandering-hyperbolic action is locally semi-rigid in the $C^0$ topology. This extends the previously established stability theory in the Lipschitz $C^0$ topology to the full $C^0$ topology. Consequently, we recover the $C^0$ -local semi-rigidity of both boundary actions of word-hyperbolic groups and cocompact lattices in semisimple Lie groups from a single dynamical principle.

Keywords

meandering hyperbolicity local semi-rigidity C0 topology boundary actions word-hyperbolic groups semisimple lie groups

Cite

@article{arxiv.2607.22216,
  title  = {Local $C^0$-semi-rigidity of meandering-hyperbolic actions},
  author = {Sungwoon Kim},
  journal= {arXiv preprint arXiv:2607.22216},
  year   = {2026}
}