3 papers
math.GR2025
Random Dehn function of groups
Jerónimo GarcÃa-MejÃa, Antoine Goldsborough
In this note, we study the notion of random Dehn function and compute an asymptotic upper bound for finitely presented acylindrically hyperbolic groups whose Dehn function is at mo…
math.GR2025
Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
Antoine Goldsborough, Mark Hagen, Harry Petyt +2
We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relat…
math.GT2024
(Non-)existence of Cannon-Thurston maps for Morse boundaries
Ruth Charney, Matthew Cordes, Antoine Goldsborough +2
We show that the Morse boundary exhibits interesting examples of both the existence and non-existence of Cannon-Thurston maps for normal subgroups, in contrast with the hyperbolic…