Growth gaps and exponential genericity in acylindrically hyperbolic groups

Lihuang Ding; Wenyuan Yang

Growth gaps and exponential genericity in acylindrically hyperbolic groups

Group Theory 2026-07-28 v1 Geometric Topology

Authors: Lihuang Ding , Wenyuan Yang

Abstract

We prove that, for every finite generating set of an acylindrically hyperbolic group, the set of non-WPD elements has strictly smaller exponential growth rate. Equivalently, WPD elements are exponentially generic. As applications, we prove growth tightness and cogrowth tightness for acylindrically hyperbolic groups.

Cite

@article{arxiv.2607.25578,
  title  = {Growth gaps and exponential genericity in acylindrically hyperbolic groups},
  author = {Lihuang Ding and Wenyuan Yang},
  journal= {arXiv preprint arXiv:2607.25578},
  year   = {2026}
}

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46 pages