Year: 2026
Type: article
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.
Source: Journal of Geometric Analysis
Author: César Rosales
Institution: Universidad de Granada
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4414828348
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