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arXiv · 2504.10413

On perimeter minimizing sets in manifolds with quadratic volume growth

Alessandro Cucinotta·Mattia Magnabosco
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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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Alessandro Cucinotta, Mattia Magnabosco. 2025-04-14. On perimeter minimizing sets in manifolds with quadratic volume growth. https://arxiv.org/abs/2504.10413

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