2 papers
math.GR2026
Small growth rates of free groups
Koji Fujiwara, Sang-hyun Kim, Ryokichi Tanaka
We introduce the notion of a Magnus marking for a finite generating set of a group and prove a certain expansion property. Using this property, we determine the second and third sm…
math.DS2025
The Manhattan curve, ergodic theory of topological flows and rigidity
Stephen Cantrell, Ryokichi Tanaka
For every non-elementary hyperbolic group, we introduce the Manhattan curve associated to any pair of left-invariant hyperbolic metrics which are quasi-isometric to a word metric.…