Convex bodies with minimal volume product in R2 - a new proof

A new proof of the Mahler conjecture in R^2 is given. In order to prove the result, we introduce a new method - the vertex removal method; i.e., for any origin-symmetric polygon P, there exists a linear image @fP contained in the unit disk B^2, and there exist three contiguous vertices of @fP lying on the boundary of B^2. We can show that the volume-product of P decreases when we remove the middle vertex of the three vertices.