Abstract
AbstractWe consider a convex solid cone $$\mathcal {C}\subset \mathbb {R}^{n+1}$$
C
⊂
R
n
+
1
with vertex at the origin and boundary $$\partial \mathcal {C}$$
∂
C
smooth away from 0. Our main result shows that a compact two-sided hypersurface $$\Sigma $$
Σ
immersed in $$\mathcal {C}$$
C
with free boundary in $$\partial \mathcal {C}\setminus \{0\}$$
∂
C
\
{
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 $$\mathcal {C}$$
C
provided the boundary of $$\Sigma $$
Σ
is away from the singular set of $$\partial \mathcal {C}$$
∂
C
.
Funder
Ministerio de Ciencia e Innovación
Consejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis