Petty's projection-volume conjecture asserts that, among convex bodies in 
of fixed volume, precisely the
ellipsoids minimize the volume
of the projection body, for every integer 
.
Equivalently, writing 
for the projection body
and 
for the volume of the unit ball
in 
,
the proposed bound is
 |
with equality iff 
is an ellipsoid. This concerns
the projection body itself, rather than its polar body.
