The Brunn-Minkowski Inequality and Related Results

Download or read book The Brunn-Minkowski Inequality and Related Results written by Trista A. Mullin and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Brunn-Minkowski Inequality is a classical result that compares the volumes of twosets, in particular convex bodies, and the volume of their Minkowski sum. The proof iselegant and the eects are far reaching in mathematics. In this thesis we will examinethe proof of the inequality, and its multiplicative and integral forms. From there wewill explore a few applications and an analog to Brunn's slice theorem. Additionally, wewill look at how the Brunn-Minkowski Inequality can be used to obtain results regardinggeneral log concave measures, isoperimetric inequalities, and spherical concentrations.We will end the journey with a quick look at what can be said about the intersectionbody of a convex body.