WILLMORE SURFACES AND LOOP GROUPS

Abstract

After a brief basic review of Willmore surfaces in §1, in §2 is shown that the conformal Gauss map plays a major role in building meromorphic potentials for these surfaces. Section §3 describes the tools of the DPW procedure, which produces the potentials by a loop group technique. The last section provides concluding remarks which outline essential differences between two perfectible approaches used to develop the presented process.