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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.