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arXiv · 2502.18788

H\"older spiral arcs

Efstathios Konstantinos Chrontsios Garitsis·Vyron Vellis
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Abstract

We establish a quantitative necessary and sufficient condition for a spiral arc to be a H\"older 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 H\"older winding problem for polynomial spirals. Moreover, we provide a sharp exponent estimate for the H\"older classification of polynomial spirals, which coincides with the corresponding quasiconformal classification estimate, and improve certain exponent bounds of Burrell-Falconer-Fraser on the H\"older classification of elliptical spirals.

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Efstathios Konstantinos Chrontsios Garitsis, Vyron Vellis. 2025-02-26. H\"older spiral arcs. https://arxiv.org/abs/2502.18788

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