The Blaschke-Santalo Inequality is a result of convex geometry concerning the Mahler volume, a dimensionless quantity associated with a centrally symmetric convex body that remains unchanged under linear transformations. The inequality establishes that, among all centrally symmetric convex bodies, the ball and the solid ellipsoids attain the largest possible Mahler volume, making them the extremal shapes for this quantity.
Facts
StatementAmong all centrally symmetric convex bodies, the ball and solid ellipsoids attain the largest possible Mahler volume. 2 Classification
Statement Form Sources
1. Wikipedia: Mahler volume
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
It is known that the shapes with the largest possible Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke-Santaló inequality.
2. Blaschke-Santalo inequality, Wikipedia
Introduction
It is known that the shapes with the largest possible Mahler volume are the balls and solid ellipsoids; this is now known as the Blaschke-Santalo inequality.
Extreme shapes
the full result was proven much later by Luis Santalo (1949)
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