Isoperimetric sets in manifolds with nonnegative Ricci curvature and Euclidean volume growth

I will present a new existence result for isoperimetric sets of  large volume on manifolds with nonnegative Ricci curvature and  Euclidean volume growth, under an additional assumption on the structure of tangent cones at infinity. After a brief discussion on the sharpness of the additional  assumption, I will show that it is always verified on manifolds with nonnegative sectional curvature. I will finally present the main ingredients of proof emphasizing the key role of nonsmooth techniques tailored for the study of RCD  spaces, a class of metric measure structures satisfying a synthetic notion of Ricci curvature bounded below. This is based on a joint work with G. Antonelli, M. Fogagnolo and M. Pozzetta.