Brunn-Minkowski-type Inequalities and Log-Convexity

This thesis builds on builds on a research paper [2]. We present basics of the Brunn-Minkowski theory for convex sets in Euclidean space. We then discuss the basics of the logarithmic Brunn-Minkowski conjecture which motivates our new result: a probabilistic extension of the dual log Brunn-Minkowski inequality due to Saroglou