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Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms

Offered By: Hausdorff Center for Mathematics via YouTube

Tags

Convex Geometry Courses Functional Analysis Courses Isoperimetric Inequalities Courses

Course Description

Overview

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.

Syllabus

Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms


Taught by

Hausdorff Center for Mathematics

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