We prove Mahler’s conjecture concerning the volume product of centrally symmetric, convex bodies in in the case where . More precisely, we show that, for every -dimensional, centrally symmetric, convex body , the volume product is greater than or equal to with equality if and only if or is a parallelepiped.
"Symmetric Mahler’s conjecture for the volume product in the -dimensional case." Duke Math. J. 169 (6) 1077 - 1134, 15 April 2020. https://doi.org/10.1215/00127094-2019-0072