Conformal Gauss Map Geometry and Application to Willmore Surfaces in Model Spaces

Abstract

In this paper we make a detailed and self-contained study of the conformalGauss map. Then, starting from the seminal work of R. Bryant and the notion of conformal Gauss map, we recover many fundamental properties of Willmore surfaces. We also get new results like some characterizations of minimal and constant meancurvature (CMC) surfaces in term of their conformal Gauss map behavior.

References in corpus (2)

• Weierstrass-Kenmotsu representation of Willmore surfaces in spheres
• Willmore surfaces in spheres: the DPW approach via the conformal Gauss map

Cited by in corpus (2)

• Minimal Bubbling for Willmore Surfaces
• Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications