AI 中文总结
研究蜿蜒双曲作用的局部 $C^0$-半刚性问题，通过证明其在该拓扑下的局部半刚性，将稳定性理论从利普希茨 $C^0$ 拓扑扩展到完整 $C^0$ 拓扑，进而从单一原理恢复相关作用及格的 $C^0$-局部半刚性。
AI 中文摘要
卡波维奇、金和李引入的蜿蜒双曲性将经典双曲性扩展到字双曲群之外。本文证明了每个蜿蜒双曲作用在 $C^0$ 拓扑中是局部半刚性的，将先前在利普希茨 $C^0$ 拓扑中建立的稳定性理论扩展到完整的 $C^0$ 拓扑。从而从单一动力学原理恢复了字双曲群的边界作用和半单李群中共紧格的 $C^0$-局部半刚性。
英文摘要
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.
