ORIGIN-SYMMETRIC BODIES OF REVOLUTION WITH MINIMAL MAHLER VOLUME IN R 3 -A NEW PROOF

In (22), Meyer and Reisner proved the Mahler conjecture for rovelution bodies. In this paper, using a new method, we prove that among origin-symmetric bodies of revolution in R 3 , cylinders have the minimal Mahler volume. Further, we prove that among parallel sections homothety bodies in R 3 , 3-cubes have the minimal Mahler volume.