Adolfo Arroyo-Rabasa

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20212025

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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…

math.AP2024

Local Poincaré constants and mean oscillation functionals for $B V$ functions

Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin

We introduce the concept of local Poincaré constant of a $B V$ function as a tool to understand the relation between its mean oscillation and its total variation at small scales. Th…

math.AP2021

Representation of the total variation as a $Γ$ -limit of $B M O$ -type seminorms

Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin

We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the $Γ$ -limit, with respect to the $L_{loc}^{1}$ topology, of a family of $B M O$ -type seminor…

Structural properties of one-dimensional metric currents: SBV-representations, connectedness and the flat chain conjecture

Local Poincaré constants and mean oscillation functionals for BV functions

Representation of the total variation as a Γ-limit of BMO-type seminorms

Local Poincaré constants and mean oscillation functionals for $B V$ functions

Representation of the total variation as a $Γ$ -limit of $B M O$ -type seminorms