We review recent results on the study of the isoperimetric problem on Riemannian manifolds
with Ricci lower bounds. We focus on the validity of sharp second order differential …

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic
isoperimetric properties for small and large volumes on N-dimensional RCD (K, N) spaces …

This paper studies sharp isoperimetric comparison theorems and sharp dimensional
concavity properties of the isoperimetric profile for non smooth spaces with lower Ricci …

We review recent results regarding the problem of the stability of Sobolev inequalities on
Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and …

The title is meant as way to honor two great mathematicians that, although never actually
worked together, introduced concepts of convergence that perfectly match each other and …

We establish a structure theorem for minimizing sequences for the isoperimetric problem on
noncompact RCD (K, N) spaces (X, d, ℋ N). Under the sole (necessary) assumption that the …

The sharp isoperimetric inequality for non-compact Riemannian manifolds with nonnegative
Ricci curvature and Euclidean volume growth has been obtained in increasing generality …

We prove that if M is a closed n-dimensional Riemannian manifold, n≥ 3, with Ric≥ n-1 and
for which the optimal constant in the critical Sobolev inequality equals the one of the n …

We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying
the synthetic Ricci curvature lower bounds Measure Contraction property ($\mathsf {MCP}(0 …

In this paper we consider Riemannian manifolds of dimension at least $3 $, with
nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset …