Harmonic map methods for Willmore surfaces

TL;DR

This paper explores how harmonic map techniques, inspired by constant mean curvature surfaces, can be applied to study Willmore surfaces, providing new insights into their geometric properties.

Contribution

It introduces a novel approach linking harmonic Gauss maps to Willmore surfaces, enhancing understanding of their structure and properties.

Findings

Harmonic map analogy yields new results on Willmore surfaces

Provides a framework connecting harmonic Gauss maps to Willmore surface analysis

Advances geometric understanding of Willmore surfaces through harmonic methods

Abstract

In this note we demonstrate how the analogy between the harmonic Gauss map of a constant mean curvature surface and the harmonic conformal Gauss map of a Willmore surface can be used to obtain results on Willmore surfaces.