Compact anisotropic stable hypersurfaces with free boundary in convex solid cones
Metadata
Show full item recordEditorial
Springer Nature
Materia
Convex solid cone Anisotropic area Free boundary Stable hypersurface
Date
2023-07-03Referencia bibliográfica
Rosales, C. Compact anisotropic stable hypersurfaces with free boundary in convex solid cones. Calc. Var. 62, 185 (2023). [https://doi.org/10.1007/s00526-023-02528-0]
Sponsorship
Grant PID2020-118180GB-I00 funded by MCIN/AEI/10.13039/501100011033; Junta de Andalucía grant PY20-00164Abstract
We consider a convex solid cone C in R^{n+1} with vertex at the origin and boundary smooth away from 0. Our main result shows that a compact two-sided hypersurface Sigma immersed in C with free boundary away from 0 and minimizing, up to second order, an anisotropic area functional under a volume constraint is contained in a Wulff-shape. The technique of proof also works for a non-smooth convex cone C provided the boundary of Sigma is away from the singular set of the boundary of C.