On perimeter minimizing sets in manifolds with quadratic volume growth

Journal article

Abstract This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold ( M , g ) (M,g) forces an isometric splitting. We show that this is the case when 𝑀 has non-negative sectional curvature and quadratic volume growth at infinity. Moreover, we obtain that the boundary of the perimeter minimizing set is identified with a slice in the product structure of 𝑀.

Authors: Cucinotta, A; Magnabosco, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: De Gruyter
• Journal: Journal für die reine und angewandte Mathematik
• Volume: 0
• Publication date: 2026-04-02
• DOI: 10.1515/crelle-2026-0017
• EISSN: 1435-5345
• ISSN: 0075-4102
• Language: English
• Keywords: Perimeter; Curvature; Set (abstract data type); Quadratic equation; Product (mathematics); Boundary (topology); Manifold (fluid mechanics); Volume (thermodynamics)