Résumé
We give a new integral formula for the centro-projective area of a convex body, which was first defined by Berck-Bernig-Vernicos. We then use the formula to prove that it is bounded from above by the centro-projective area of an ellipsoid and that equality occurs if and only if the convex set is an ellipsoid. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS.