Parallel mean curvature surfaces with constant contact angle along free boundaries
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914263742808064 |
|---|---|
| author | Gao, Rui Zhu, Miaomiao |
| author_facet | Gao, Rui Zhu, Miaomiao |
| contents | We classify branched immersed disks in space forms with non-zero parallel mean curvature vector and non-orthogonal constant contact angle along the boundary in 4-dimensional space form. For higher codimensional case, we prove a codimension reduction theorem for branched immersed bordered Riemann surfaces of higher genus with multiple boundary components under the same parallel mean curvature and constant contact angle assumptions. Furthermore, we construct a family of explicit examples of branched minimal immersions satisfying the non-orthonormal constant contact angle free boundary condition, which demonstrate the sharpness of both the classification result and the codimension reduction result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13101 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parallel mean curvature surfaces with constant contact angle along free boundaries Gao, Rui Zhu, Miaomiao Differential Geometry 49J35, 53A10, 53C42, 58E20 We classify branched immersed disks in space forms with non-zero parallel mean curvature vector and non-orthogonal constant contact angle along the boundary in 4-dimensional space form. For higher codimensional case, we prove a codimension reduction theorem for branched immersed bordered Riemann surfaces of higher genus with multiple boundary components under the same parallel mean curvature and constant contact angle assumptions. Furthermore, we construct a family of explicit examples of branched minimal immersions satisfying the non-orthonormal constant contact angle free boundary condition, which demonstrate the sharpness of both the classification result and the codimension reduction result. |
| title | Parallel mean curvature surfaces with constant contact angle along free boundaries |
| topic | Differential Geometry 49J35, 53A10, 53C42, 58E20 |
| url | https://arxiv.org/abs/2601.13101 |