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math.MG2025
Quasisymmetric rectifiability of uniformly disconnected sets
Jacob Honeycutt, Vyron Vellis
We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological…
math.CA2025
Hölder spiral arcs
Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis
We establish a quantitative necessary and sufficient condition for a spiral arc to be a Hölder arc. The class of spiral arcs contains the polynomial spirals studied by Fraser, and…