On Some Tight Convexity Inequalities for Symmetric Convex Sets

Explore a lecture on tight convexity inequalities for symmetric convex sets, delivered by Galyna Livshyts at the Hausdorff Center for Mathematics. Delve into a conjectured inequality strengthening the Ehrhard inequality for symmetric convex sets in the case of standard Gaussian measure. Examine its connections to isoperimetric problems and the Dirichlet-Poincare inequality, with round k-cylinders as optimizers. Investigate progress using L2 methods, energy minimization, and related estimates. Learn about equality case characterization based on quantitative stability in energy minimization and the Brascamp-Lieb inequality. Discover new inequalities for other measures and gain insights into topics such as the Minkowski inequality, Gaussian symmetric cases, and correlation inequalities.

Intro
Minkowski inequality
General idea
Gaussian symmetric
Explicit version
Parametric inequality
S inequality
dimensional minkowski conjecture
results
Correlation inequality
Questions
Main result
Proof
Minimize
Torsional rigidity
Brass complement equality
Summary of results