  The width of a closed convex subset of Euclidean space is the distance
between two parallel supporting planes. The Blaschke-Lebesgue problem consists
of minimizing the volume in the class of convex sets of fixed constant width
and is still open in dimension n > 2. In this paper we describe a necessary
condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension
n=3: we prove that the smooth components of the boundary of the minimizer have
their smaller principal curvature constant, and therefore are either spherical
caps or pieces of tubes (canal surfaces).
