Compact anisotropic stable hypersurfaces with free boundary in convex solid cones Rosales Lombardo, Manuel César Convex solid cone Anisotropic area Free boundary Stable hypersurface 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. 2023-07-03T07:55:18Z 2023-07-03T07:55:18Z 2023-07-03 journal article 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] https://hdl.handle.net/10481/83044 10.1007/s00526-023-02528-0 eng http://creativecommons.org/licenses/by-nc/4.0/ open access Atribución-NoComercial 4.0 Internacional Springer Nature