Willmore surfaces in spheres via loop groups: a survey

Autor:	Dorfmeister, Josef F., Wang, Peng
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry 53A30 53C30 53C35
Druh dokumentu:	Working Paper
Popis:	In the past decades, the authors made some systematic research on global and local properties of Willmore surfaces in terms of the DPW method. In this note we give a survey, mainly including the basic framework of the DPW method for the global geometry of Willmore surfaces via the conformal Gauss map, applications on constructions of Willmore $2$-spheres, characterizations of minimal surfaces, Willmore deformations of Willmore surfaces and Bjoerling problems for Willmore surfaces. Moreover, we also obtained some results on harmonic maps via DPW, including a duality theorem for harmonic maps into an inner non-compact symmetric space and its dual inner compact symmetric space, and harmonic maps of finite uniton type. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.10831 Zobrazit plný text záznamu View this record from Arxiv