On perimeter minimizing sets in manifolds with quadratic volume growth

2025/04/14 by Alessandro Cucinotta, Cucinotta, Alessandro, Mattia Magnabosco +1
Mathematics · Computer Science · #Point processes and geometric inequalities #Mathematical Dynamics and Fractals #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2504.10413

Abstract

This paper studies whether the presence of a perimeter minimizing set in a Riemannian manifold (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.

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