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.
Cucinotta et al. (Thu,) studied this question.