arXiv subjects

Lihuang Ding

Publications and source records attributed to Lihuang Ding.

4 recordsLinked to original sources

arXiv2026

Growth gaps and exponential genericity in acylindrically hyperbolic groups

Let $G$ be a finitely generated group acting by isometries on a geodesic metric space with two independent strongly contracting WPD elements. We prove that, for every finite generating set of $G$, strongly contracting WPD elements for this action are exponentially generic in word-metric balls. The proof establishes a growth gap for elements with small displacement relative to word length in an auxiliary projection complex. For finitely generated acylindrically hyperbolic groups, we establish growth tightness and cogrowth tightness for every finite generating set. We also show that the number of conjugacy classes meeting a ball of radius $n$ is comparable to the cardinality of that ball divided by $n$.

math.GR↗

arXiv2026

Growth Gaps for Quotients by Confined Subgroups

In this paper, we establish growth gaps for quotients by confined subgroups in groups admitting a statistically convex-cocompact action with contracting elements. We also discuss applications to uniformly recurrent subgroups.

math.GR↗

arXiv2026

Sublinear projection tracking in acylindrically hyperbolic groups

We study projection phenomena in word metrics of finitely generated acylindrically hyperbolic groups. For a loxodromic WPD element acting on a hyperbolic space, we prove that shortest projection in the word metric to the corresponding cyclic subgroup sublinearly tracks the pullback of shortest projection to its axis in the hyperbolic space. As applications, we obtain effective upper bounds for growth functions and construct proper quotients whose growth rates converge to that of the original group. We further prove a growth--cogrowth inequality for confined subgroups in both acylindrically hyperbolic groups and Morse local-to-global groups with Morse elements.

math.GR↗

arXiv2025

Growth tightness and genericity for word metrics from injective spaces

Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show that all finite generating sets resulting from taking large enough balls in the respective injective space yield word metrics where pseudo-Anosov maps are exponentially generic. We also show that growth tightness holds true for the Cayley graphs corresponding to these finite generating sets, providing a positive answer to a question by Arzhantseva, Cashen and Tao.

math.GT↗