On the classification of capillary graphs in Euclidean and non-Euclidean spaces

Giulio Colombo; Alberto Farina; Marco Magliaro; Luciano Mari; Marco Rigoli

On the classification of capillary graphs in Euclidean and non-Euclidean spaces

Differential Geometry 2025-12-22 v1 Analysis of PDEs

Authors: Giulio Colombo , Alberto Farina , Marco Magliaro , Luciano Mari , Marco Rigoli

Abstract

We prove some rigidity and classification results for graphs with prescribed mean curvature and locally constant Dirichlet and Neumann data, for instance as they appear in capillarity problems. We consider domains in Riemannian manifolds, with emphasis on $\mathbb{R}^2$ and $\mathbb{R}^3$ . We classify both the underlying domain and the resulting solution, providing general splitting theorems in this setting.

Keywords

capillary graphs mean curvature Dirichlet boundary condition Neumann boundary condition classification Riemannian manifolds

Cite

@article{arxiv.2512.17813,
  title  = {On the classification of capillary graphs in Euclidean and non-Euclidean spaces},
  author = {Giulio Colombo and Alberto Farina and Marco Magliaro and Luciano Mari and Marco Rigoli},
  journal= {arXiv preprint arXiv:2512.17813},
  year   = {2025}
}

Comments

54 pages (but the last is just two lines), 2x2 figures. Package axessibility included to make the paper available to visually impaired people

On the classification of capillary graphs in Euclidean and non-Euclidean spaces

Abstract

Keywords

Cite

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