Journal of Geometric Analysis· 2026Q1
Some Remarks on Singular Capillary Cones with Free Boundary
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- Q1SCImago
- 2026year
Short summary
Minimizing capillary cones are proven to be flat under specific mean curvature conditions (non-negative for n≤4, non-positive for n≤6) and in dimensions up to 6 for axially symmetric cases.
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Key points
- Minimizing capillary cones are flat if free boundary mean curvature is non-negative and n≤4.
- Minimizing capillary cones are flat if free boundary mean curvature is non-positive and n≤6.
- Axially symmetric minimizing cones are flat in dimensions up to 6.
- Improved regularity results are derived for graphical minimizing capillary hypersurfaces.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Journal of Geometric Analysis, 2026 · DOI ↗
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Computational Theory and MathematicsComputer Science