Symmetric Mahler’s conjecture for the volume product in the 3-dimensional case
Hiroshi Iriyeh, Masataka Shibata
Abstract
We prove Mahler’s conjecture concerning the volume product of centrally symmetric, convex bodies in Rn in the case where n=3. More precisely, we show that, for every 3-dimensional, centrally symmetric, convex body K⊂R3, the volume product |K||K∘| is greater than or equal to 32/3 with equality if and only if K or K∘ is a parallelepiped.
Topics & Concepts
MathematicsConjectureProduct (mathematics)Convex bodyMixed volumeRegular polygonVolume (thermodynamics)CombinatoricsPure mathematicsConvex setConvex geometryConvex combinationMathematical analysisProduct topologyConvex analysisMinimal volumePoint processes and geometric inequalitiesAdvanced Combinatorial MathematicsGeometric Analysis and Curvature Flows