Graduate Student Seminars
Title: Some extensions of the Brunn-Minkowski inequality
Abstract: The Brunn-Minkowski inequality states that for any measurable sets K and L, the volume of (K+L)/2 is lower bounded by the geometric mean of the volume of K and the volume of L. I will discuss some far reaching extensions of this inequality established in the early 20th century, such as Minkowski’s first and second inequality and the Alexandrov-Fenchel inequality. And if time permits, I will discuss a more recent conjectural extension called the logarithmic Brunn-Minkowski inequality.