English

Willmore surfaces in spheres: the DPW approach via the conformal Gauss map

Differential Geometry 2019-03-05 v1

Abstract

The paper builds a DPW approach of Willmore surfaces via conformal Gauss maps. As applications, we provide descriptions of minimal surfaces in Rn+2\mathbb R^{n+2}, isotropic surfaces in S4S^4 and homogeneous Willmore tori via the loop group method. A new example of a Willmore two-sphere in S6S^6 without dual surfaces is also presented.

Keywords

Cite

@article{arxiv.1903.00883,
  title  = {Willmore surfaces in spheres: the DPW approach via the conformal Gauss map},
  author = {Josef F. Dorfmeister and Peng Wang},
  journal= {arXiv preprint arXiv:1903.00883},
  year   = {2019}
}

Comments

23 pages. Following the suggestion of some anonymous referee we have divided the paper entitled "Willmore surfaces in spheres via loop groups I: generic cases and some examples" (arXiv:1301.2756) into three parts. The present paper is part II and [15,16] are part I and part III respectively