Fourier series of circle embeddings

TL;DR

This paper investigates the Fourier series of circle embeddings, focusing on Blaschke product approximation and Fourier coefficient behavior, linking these properties to geometric features and minimal surface curvature.

Contribution

It introduces new insights into the Fourier series of circle embeddings, particularly regarding Blaschke products and coefficient vanishing, connecting analytic and geometric aspects.

Findings

Fourier coefficients can vanish under certain conditions.

Blaschke product approximation is effective for circle embeddings.

Analytic properties relate to the geometry and curvature of minimal surfaces.

Abstract

We study the Fourier series of circle homeomorphisms and circle embeddings, with the emphasis on Blaschke product approximation and the vanishing of Fourier coefficients. The analytic properties of the Fourier series are related to the geometry of the circle embeddings, and have implications for the curvature of minimal surfaces.