Some Remarks on Singular Capillary Cones with Free Boundary
Abstract
Abstract We study singular minimizing capillary cones with free boundary. We provide a stability criterion à la Jerison–Savin and use it to prove that a minimizing capillary cone is flat when its free boundary mean curvature is non-negative and $$n\le 4$$ n ≤ 4 , or non-positive and $$n\le 6$$ n ≤ 6 . We also show that minimizing cones with axially symmetric free boundary are flat in dimensions up to $$6$$ 6 , and derive improved regularity results for graphical minimizing capillary hypersurfaces. The proofs rely on Simons-type inequalities for convex, homogeneous, symmetric functions of the principal curvatures, coupled with a boundary identity intrinsic to the capillary setting.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Geometric Analysis and Curvature Flows
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Journal of Geometric Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 11
- Publication date
- 22 September 2026
- Language
- EN