Year: 2026
Type: article
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.
Source: Journal of Geometric Analysis
Institutions: ETH Zurich, University of Turin, University of Pisa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4407425812