Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

On Some Tight Convexity Inequalities for Symmetric Convex Sets

Hausdorff Center for Mathematics via YouTube

Overview

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.

Syllabus

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

Taught by

Hausdorff Center for Mathematics

Reviews

Start your review of On Some Tight Convexity Inequalities for Symmetric Convex Sets

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.