Work

On perimeter minimizing sets in manifolds with quadratic volume growth

Year: 2026

Type: 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.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2026-0017

Authors: Alessandro Cucinotta, Mattia Magnabosco

Institution: University of Oxford

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: Royal Society, Hausdorff Center for Mathematics