On the Anisotropic Partitioning Problem in Euclidean Convex Domains
Abstract
Abstract We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features about the minimizers and sharp isoperimetric inequalities with respect to convex cones. Besides some known geometric measure theory results about the existence and regularity of minimizers, the proofs strongly rely on a second variation formula for the anisotropic area of hypersurfaces with non-empty boundary.
Fields of Study & Subjects
Analytic and geometric function theory
Publication details
- Journal / source
- Journal of Geometric Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 7
- Publication date
- 27 May 2026
- Language
- EN