“…Therefore, all of our results apply in this setting. While the existence of 1‐Cheeger sets was already known, see [
51, 86], and the clustering isoperimetric problem has been recently addressed in [
106], the Cheeger cluster problem for
had never been treated. The relation with the prescribed curvature functional had been studied in [
51], while, up to our knowledge, the relation with the first eigenvalue of the Dirichlet
‐Laplacian had never been proved, but only quickly observed in [
86] for
(the Ornstein–Uhlenbeck operator).…”