Feb 23. 2022, 16:20 — 16:55

We discuss the existence of generalized clusters with a finite or infinite number of components, having minimal total perimeter and given masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms. Such clusters are a natural relaxation of a cluster and can be thought of as "albums" with possibly infinite pages, the total perimeter being calculated by summation over all pages, and being minimal among all generalized clusters with the same masses.