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Lower bound for the perimeter density at singular points of a minimizing cluster in R^n

Michele Marini
Institution: 
SISSA
Location: 
A-133
Schedule: 
Friday, March 16, 2018 - 14:00
Abstract: 

A cluster is a partition of $\mathbb{R}^n$ into a finite family of sets of finite perimeter called chambers. We shall study the singular points of minimizing clusters (i.e. partitions minimizing the perimeter under some volume constraints); in particular we shall investigate the peculiar behavior of the singular points lying in the boundary of three or more chambers. In the talk we will establish a dimension-free lower bound for the perimeter density at those "special" singular points and we will discuss some applications. The results are obtained in collaboration with Jonas Hirsch.  

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