3 papers
math.GR2025
Groups with a finite Busemann boundary are virtually cyclic
Corentin Bodart, Liran Ron-George, Ariel Yadin
This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a C…
math.GR2024
Detecting virtual homomorphisms via Banach metrics
Liran Ron-George, Ariel Yadin
We introduce the notion of "Banach metrics" on finitely generated infinite groups. This extends the notion of a Cayley graph (as a metric space). Our motivation comes from trying t…
math.GR2023
Groups with finitely many Busemann points
Liran Ron-George, Ariel Yadin
We show that an infinite finitely generated group G is virtually-Z if and only if every Cayley graph of G contains only finitely many Busemann points in its horofunction boundary.…