2 problems

Let $\mathcal C(1,1,1,1)$ denote the stationary planar clusters with four regions of area $1$, and let a sandwich-topology cluster be one with the topology described in the source.…

Let $N$ be a positive integer, let $\boldsymbol a\in\mathbb{R}^N_+$ be a vector of prescribed positive areas, and let $\mathcal M(\boldsymbol a)$ denote the set of perimeter-minimi…