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math.AP2025
Affine rigidity of functions with additive oscillation
Adolfo Arroyo-Rabasa, Sergio Conti
We prove that a locally integrable function must be affine if its mean oscillation, considered as a function of intervals, can be extended to a locally fini…
math.AP2025
Structural properties of one-dimensional metric currents: SBV-representations, connectedness and the flat chain conjecture
Adolfo Arroyo-Rabasa, Guy Bouchitté
A comprehensive study of one-dimensional metric currents and their relationship to the geometry of metric spaces is presented. We resolve the one-dimensional flat chain conjecture…