# The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis

@inproceedings{Antonelli2021TheIP, title={The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis}, author={Gioacchino Antonelli and Mattia Fogagnolo and Marco Pozzetta}, year={2021} }

In this paper we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below and with a mild assumption at infinity, that is Gromov–Hausdorff asymptoticity to simply connected models of constant sectional curvature. The previous result is a consequence of a general structure theorem for perimeterminimizing sequences of sets of fixed volume on noncollapsed Riemannian manifolds with a lower bound on the Ricci curvature. We show that, without… Expand

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