R. Arnold and -. Wellerding, On the Sobolev distance of convex bodies, Aequationes Math, pp.72-83, 1992.

J. D. Bourgain-v and . Milman, New volume ratio properties for convex symmetric bodies in ? n, Inventiones Mathematicae, vol.40, issue.13, pp.319-340, 1987.
DOI : 10.1007/BF01388911

K. J. Böröczky, E. Makai, J. , M. Meyer, and S. Reisner, On the volume product of planar polar convex bodies ??? Lower estimates with stability, Studia Scientiarum Mathematicarum Hungarica, vol.50, issue.2, pp.159-198, 2013.
DOI : 10.1556/SScMath.50.2013.2.1235

D. Bucur-i and . Fragaì-a-j, Lamboley -Optimal convex shapes for concave functionals, ESAIM Control Optim. Calc. Var, pp.693-711, 2012.

J. Kim-s, LOCAL MINIMALITY OF THE VOLUME-PRODUCT AT??THE SIMPLEX, Mathematika, vol.8, issue.01, pp.121-134, 2011.
DOI : 10.1111/j.1749-6632.1985.tb14545.x

T. Lachand-robert and M. A. Peletier, -Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions, Modeling, Analysis and Simulation, pp.1-19, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00385121

J. Lamboley-a, Polygons as Optimal Shapes with Convexity Constraint, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3003-3025, 2009.
DOI : 10.1137/080738581

Y. Lin-g, Leng -Convex bodies with minimal volume product in R 2 -a new proof, Discrete Mathematics 310, pp.3018-3025, 2010.

M. Meyer-s, Shadow Systems and Volumes of Polar Convex Bodies, Mathematika, vol.44, issue.01, pp.129-148, 2007.
DOI : 10.1007/BF01199119

F. Nazarov-f, . Petrov-d, and . Ryabogin-a, Zvavitch -A remark on the Mahler conjecture: local minimality of the unit cube, Duke Math, J, vol.154, issue.3, pp.419-430, 2010.

L. A. Santaló, Un invariante afin para los cuerpos convexos del espacio de n dimensiones, Portugal. Math, vol.8, pp.155-161, 1949.

A. Stancu, Two Volume Product Inequalities and Their Applications, Bulletin canadien de math??matiques, vol.52, issue.3, pp.464-472, 2009.
DOI : 10.4153/CMB-2009-049-0

R. Schneider, Convex bodies: The Brunn-Minkowski Theory, 1993.
DOI : 10.1017/CBO9780511526282

S. Reisner, Zonoids with minimal volume-product, Mathematische Zeitschrift, vol.14, issue.3, pp.339-346, 1986.
DOI : 10.1007/BF01164009

S. Reisner, C. Schütt, and E. M. Werner, Mahler's Conjecture and Curvature, International Mathematics Research Notices, vol.2012, issue.1, pp.1-16
DOI : 10.1093/imrn/rnr003

T. Tao, open-problem-the-mahler-conjecture-on-convex-bodies, 2007.