Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature

@article{Balogh2022SharpIA,
  title={Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature},
  author={Zolt'an M. Balogh and Alexandru Krist'aly},
  journal={Mathematische Annalen},
  year={2022}
}
By using optimal mass transport theory we prove a sharp isoperimetric inequality in CD(0, N) metric measure spaces assuming an asymptotic volume growth at infinity. Our result extends recently proven isoperimetric inequalities for normed spaces and Riemannian manifolds to a nonsmooth framework. In the case of n-dimensional Riemannian manifolds with nonnegative Ricci curvature, we outline an alternative proof of the rigidity result of S. Brendle (2021). As applications of the isoperimetric… 
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References

SHOWING 1-10 OF 72 REFERENCES
Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
In this paper we consider complete noncompact Riemannian manifolds $(M, g)$ with nonnegative Ricci curvature and Euclidean volume growth, of dimension $n \geq 3$. We prove a sharp Willmore-type
Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition
We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below (possibly negatively), and
Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds
abstract:We study a Riemannian manifold equipped with a density which satisfies the Bakry-\'Emery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an
On complete manifolds with nonnegative Ricci curvature
Complete open Riemannian manifolds (Mn, g) with nonnegative sectional curvature are well understood. The basic results are Toponogov's Splitting Theorem and the Soul Theorem [CG1]. The Splitting
Lower bounds on Ricci curvature and the almost rigidity of warped products
The basic rigidity theorems for manifolds of nonnegative or positive Ricci curvature are the "volume cone implies metric cone" theorem, the maximal diameter theorem, [Cg], and the splitting theorem,
Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below
On manifolds with non-negative Ricci curvature and Sobolev inequalities
— Let M be a complete n-dimensional Riemanian manifold with non-negative Ricci curvature in which one of the Sobolev inequalities (∫ |f |dv )1/p ≤ C(∫ |∇f |qdv)1/q, f ∈ C∞ 0 (M), 1 ≤ q 1. Moreover,
Manifolds of positive Ricci curvature with almost maximal volume
10. In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below. The well-known theorems of Myers and Bishop imply that a manifold Mn with Ric > n 1 satisfies
Sharp isoperimetric inequalities via the ABP method
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp
Ricci curvature and volume convergence
The purpose of this paper is to give a new (integral) estimate of distances and angles on manifolds with a given lower Ricci curvature bound. This will provide us with an integral version of the
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