On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

Gioacchino Antonelli; Elia Bruè; Mattia Fogagnolo; Marco Pozzetta

doi:10.1007/s00526-022-02193-9

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arXiv · 2107.07318

On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

Gioacchino Antonelli·Elia Bruè·Mattia Fogagnolo·Marco Pozzetta

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Abstract

In this paper we provide new existence results for isoperimetric sets of large volume in Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth. We find sufficient conditions for their existence in terms of the geometry at infinity of the manifold. As a byproduct we show that isoperimetric sets of big volume always exist on manifolds with nonnegative sectional curvature and Euclidean volume growth. Our method combines an asymptotic mass decomposition result for minimizing sequences, a sharp isoperimetric inequality on nonsmooth spaces, and the concavity property of the isoperimetric profile. The latter is new in the generality of noncollapsed manifolds with Ricci curvature bounded below.

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Gioacchino Antonelli, Elia Bruè, Mattia Fogagnolo, Marco Pozzetta. 2021-07-15. On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. https://doi.org/10.1007/s00526-022-02193-9

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