Convex bodies with minimal volume product in — a new proof

Abstract: A new proof of the Mahler conjecture in is given. In order to prove the result, we introduce a new method — the vertex removal method; i.e., for any origin-symmetric polygon , there exists a linear image contained in the unit disk , and there exist three contiguous vertices of lying on the boundary of . We can show that the volume-product of decreases when we remove the middle vertex of the three vertices. [ABSTRACT FROM AUTHOR]