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.
Mahler,Ein Übertragungsprinzip für konvexe Körper, Časopis pro pěstování matematiky a fysiky68 (1939), 93–102
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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.