Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416043348
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