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arXiv · 2511.20495

Groups with a finite Busemann boundary are virtually cyclic

Corentin Bodart·Liran Ron-George·Ariel Yadin
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Abstract

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 Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic. Together with previous works, this completes the full characterization of groups with finite metric-functional boundaries. The main new notion introduced is that of annihilators.

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Corentin Bodart, Liran Ron-George, Ariel Yadin. 2025-11-25. Groups with a finite Busemann boundary are virtually cyclic. https://doi.org/10.1112/blms.70462

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