The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds

Gioacchino Antonelli, Stefano Nardulli, Marco Pozzetta

We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},{\mathcal{H}}^N)$. Under the sole (nec…