Varifolds with capillary boundary
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908283313324032 |
|---|---|
| author | Wang, Guofang Zhang, Xuwen |
| author_facet | Wang, Guofang Zhang, Xuwen |
| contents | In this paper we introduce and study a new class of varifolds in $\mathbf{R}^{n+1}$ of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon measure on a subspace of the trivial Grassmannian bundle over the supporting hypersurface as a generalized boundary with prescribed angle, which plays a role as a measure-theoretic capillary boundary. We show several structural properties, monotonicity inequality, boundary rectifiability, classification of tangent cones, and integral compactness for such varifolds under reasonable conditions. This Neumann-type boundary condition fits very well in the context of curvature varifold and Brakke flow, which we also discuss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Varifolds with capillary boundary Wang, Guofang Zhang, Xuwen Differential Geometry 49Q15, 53C42 In this paper we introduce and study a new class of varifolds in $\mathbf{R}^{n+1}$ of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon measure on a subspace of the trivial Grassmannian bundle over the supporting hypersurface as a generalized boundary with prescribed angle, which plays a role as a measure-theoretic capillary boundary. We show several structural properties, monotonicity inequality, boundary rectifiability, classification of tangent cones, and integral compactness for such varifolds under reasonable conditions. This Neumann-type boundary condition fits very well in the context of curvature varifold and Brakke flow, which we also discuss. |
| title | Varifolds with capillary boundary |
| topic | Differential Geometry 49Q15, 53C42 |
| url | https://arxiv.org/abs/2503.19052 |