Hölder spiral arcs

Abstract

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.

11 pages, proved a more general theorem in Section 3