Local C⁰-semi-rigidity of meandering-hyperbolic actions

2026/07/24 by Sungwoon Kim
Mathematics · #math.GT #math.GR

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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 C⁰ topology. This extends the previously established stability theory in the Lipschitz C⁰ topology to the full C⁰ topology. Consequently, we recover the C⁰-local semi-rigidity of both boundary actions of word-hyperbolic groups and cocompact lattices in semisimple Lie groups from a single dynamical principle.

Related

• Structural stability of meandering-hyperbolic group actions
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