The non-symmetric Mahler conjecture holds in dimension three: the volume product P(K) satisfies P(K) >= 64/9 for every convex body K in R^3.
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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 non-symmetric Mahler conjecture holds in dimension three: the volume product P(K) satisfies P(K) >= 64/9 for every convex body K 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.