Lower bound for the perimeter density at singular points of a minimizing cluster in ${\mathbb{R}}^N$

Abstract

In this paper we study the blow-ups of the singular points in the boundary of a minimizing cluster lying in the interface of more than two chambers. We establish a sharp lower bound for the perimeter density at those points and we prove that this bound is rigid, namely having the lowest possible density completely characterizes the blow-up.

References in corpus (1)

• Proof of the Double Bubble Conjecture in R^n