  We analyze aspects of the behavior of the family of inner parallel bodies of
a convex body for the isoperimetric quotient and deficit of arbitrary
quermassintegrals. By means of technical boundary properties of the so-called
form body of a convex body and similar constructions for inner parallel bodies,
we point out an erroneous use of a relation between the latter bodies in two
different works. We correct these results, limiting them to convex bodies
having a very precise boundary structure.
