A NEW LOWER BOUND FOR THE VOLUME PRODUCT OF A CONVEX BODY WITH CONSTANT WIDTH AND POLAR DUAL OF ITS p-CENTROID BODY Chai, Y.D.; Lee, Young-Soo;
In this paper, we prove that if K is a convex body in and and are inscribed ellipsoid and circumscribed ellipsoid of K respectively with , then . Lutwak and Zhang proved that if K is a convex body, if and only if K is an ellipsoid. Our inequality provides very elementary proof for their result and this in turn gives a lower bound of the volume product for the sets of constant width.