Corpus ID: 231728743

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

  title={The isoperimetric problem on Riemannian manifolds via Gromov-Hausdorff asymptotic analysis},
  author={Gioacchino Antonelli and Mattia Fogagnolo and Marco Pozzetta},
In this paper we prove the existence of isoperimetric regions of any volume in Riemannian manifolds with Ricci bounded below assuming Gromov–Hausdorff asymptoticity to the suitable simply connected model 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 assuming any further hypotheses on… Expand

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