Willmore surfaces in spheres via loop groups: a survey
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911879492796416 |
|---|---|
| author | Dorfmeister, Josef F. Wang, Peng |
| author_facet | Dorfmeister, Josef F. Wang, Peng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Willmore surfaces in spheres via loop groups: a survey Dorfmeister, Josef F. Wang, Peng Differential Geometry 53A30, 53C30, 53C35 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. |
| title | Willmore surfaces in spheres via loop groups: a survey |
| topic | Differential Geometry 53A30, 53C30, 53C35 |
| url | https://arxiv.org/abs/2405.10831 |