2025/02/26 by Efstathios Konstantinos Chrontsios Garitsis, Garitsis, Efstathios Konstantinos Chrontsios, Vyron Vellis +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2502.18788
openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the elliptical spirals studied by Burrell-Falconer-Fraser. As an application, we recover the sharp result on the Hölder winding problem for polynomial spirals. Moreover, we provide a sharp exponent estimate for the Hölder classification of polynomial spirals, which coincides with the corresponding quasiconformal classification estimate, and improve certain exponent bounds of Burrell-Falconer-Fraser on the Hölder classification of elliptical spirals.