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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…
math.CA2018
Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem
Matthew Badger, Lisa Naples, Vyron Vellis
We investigate the geometry of sets in Euclidean and infinite-dimensional Hilbert spaces. We establish sufficient conditions that ensure a set of points is contained in the image o…