Dylan Langharst: Higher-Order Affine Isoperimetric Inequalities

Explore higher-order affine isoperimetric inequalities in this 27-minute lecture from the Hausdorff Center for Mathematics. Delve into Schneider's generalization of the difference body of a convex body to higher-order and his establishment of the higher-order analogue of the Rogers-Shephard inequality. Examine the extension of this concept to projection bodies, centroid bodies, LYZ bodies, and radial mean bodies. Discover the associated inequalities, including analogues of Zhang's projection inequality, Petty's projection inequality, the Busemann-Petty centroid inequality, Busemann's random simplex inequality, and the affine Sobolev inequality. Learn about the collaborative research conducted with J. Haddad, E. Putterman, M. Roysdon, and D. Ye in this advanced mathematical exploration.