Convex bodies with minimal volume product in R^2-a new proof

Youjiang Lin

Convex and Discrete Geometry mathscidoc:1703.40024

Discrete Mathematics
A new proof of the Mahler conjecture in R2 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 P contained in the unit disk B2, and there exist three contiguous vertices of P lying on the boundary of B2. We can show that the volume product of P decreases when we remove the middle vertex of the three vertices.
Mahler conjecture
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@inproceedings{youjiangconvex,
  title={Convex bodies with minimal volume product in R^2-a new proof},
  author={Youjiang Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304213000711276610},
  booktitle={Discrete Mathematics},
}
Youjiang Lin. Convex bodies with minimal volume product in R^2-a new proof. In Discrete Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304213000711276610.
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