Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms

Explore a 43-minute lecture on advanced topics in convex geometric analysis, focusing on the Blaschke–Santaló inequality and its extensions. Delve into new isoperimetric inequalities for monotone Minkowski endomorphisms of convex bodies, examining their relationship to the classical Euclidean Urysohn inequality. Investigate the unique position of the Blaschke–Santaló inequality as the strongest and only affine invariant inequality within this family. Discover the limitations of extending these inequalities to weakly monotone Minkowski endomorphisms and the unexpected implications of this finding. Learn about a new set of analytic inequalities for Asplund endomorphisms of log-concave functions, which generalize the functional Blaschke–Santaló inequality. Gain insights into cutting-edge research in geometric analysis through this collaborative work presented by Franz Schuster at the Hausdorff Center for Mathematics.