Volume 26, 2020
|Number of page(s)||15|
|Published online||09 January 2020|
Lower bound for the perimeter density at singular points of a minimizing cluster in ℝN★
Mathematisches Institut, Universität Leipzig,
Augustus Platz 10,
2 Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy.
* Corresponding author: firstname.lastname@example.org
Accepted: 18 January 2019
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.
Mathematics Subject Classification: 49Q05 / 49Q20 / 53A10
Key words: Isoperimetric problems / partitioning problems / minimal surfaces
© EDP Sciences, SMAI 2020
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