4 problems

A stable regular cluster is a regular cluster that is stable under the relevant perimeter variation, and a cluster is flat when its interfaces are flat. Corneli et al.'s flatness c…

Let a $q$-cluster in $\mathbb{R}^n$ be a decomposition into $q$ cells, with $q \geq 2$ and $n \geq q-1$. The model $q$-clusters are the simplicial clusters constructed in the paper…

Let $\mathbb{S}^n$ be the unweighted round sphere, and let a $q$-cluster be a decomposition into $q$ cells of prescribed volumes. A standard spherical $(q-1)$-bubble is the stereog…

Let a $q$-cluster be a decomposition of $mathbb{R}^n$ into pairwise disjoint Borel cells with prescribed Gaussian measure $v in operatorname{int}Delta^{(q-1)}$, where…