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math.GR2025
Coset correct means on groups and the probability that two elements commute
Armando Martino, Motiejus Valiunas
Amenable groups are those admitting an invariant mean -- a finitely additive probability mean that assigns equal ``weight'' to any two translates of the same set. We introduce cose…
math.DG2025
Moduli spaces of flat Riemannian metrics on orbifolds
Karla García, Ingrid Amaranta Membrillo Solis, Motiejus Valiunas
We study moduli spaces of flat metrics on closed Riemannian orbifolds admitting such metrics. We show that for such orbifolds , the Teichmüller space of flat metrics $…
math.GR2025
Higher-rank GBS groups: non-positive curvature and biautomaticity
Sam Shepherd, Motiejus Valiunas
We characterise when a rank generalised Baumslag-Solitar group is CAT(0) and when it is biautomatic.