# The Brunn-Minkowski Inequality - Its Refinements and Extensions

Tuesday, October 28, 2014 - 2:00pm - 3:00pm

Arnaud Marsiglietti (University of Minnesota, Twin Cities)

The Brunn-Minkowski inequality, which states that for every non-empty

compact sets $A,B$ in $\R^n$ and every $\lambda \in [0,1]$ one has

$$ (1-\lambda)A + \lambda B^{1/n} \geq (1-\lambda)A^{1/n} + \lambda

B^{1/n}, $$

where $.$ denotes the volume (Lebesgue measure), is a fundamental

inequality in mathematics.

The aim of this talk is to present this inequality together with its

consequences, refinements and extensions.

compact sets $A,B$ in $\R^n$ and every $\lambda \in [0,1]$ one has

$$ (1-\lambda)A + \lambda B^{1/n} \geq (1-\lambda)A^{1/n} + \lambda

B^{1/n}, $$

where $.$ denotes the volume (Lebesgue measure), is a fundamental

inequality in mathematics.

The aim of this talk is to present this inequality together with its

consequences, refinements and extensions.