The paper proves the non-symmetric Mahler conjecture in dimension three by establishing the sharp lower bound of 64/9 for the non-symmetric volume product of any convex body in R^3.
Schneider,Convex Bodies: The Brunn–Minkowski Theory, second expanded edition, Encyclopedia of Mathematics and its Applications, vol
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A new proof shows that every origin-symmetric convex body K in R^3 satisfies |K| |K^o| >= 32/3 via symmetric admissible shadow systems.
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The non-symmetric Mahler conjecture in dimension three
The paper proves the non-symmetric Mahler conjecture in dimension three by establishing the sharp lower bound of 64/9 for the non-symmetric volume product of any convex body in R^3.
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The Symmetric Mahler Inequality in Dimension Three via Admissible Shadow Systems
A new proof shows that every origin-symmetric convex body K in R^3 satisfies |K| |K^o| >= 32/3 via symmetric admissible shadow systems.