It is shown that a convex body has minimal dual p-surface area among its affine transformations of the same volume if and only if its dual p-surface area measure is isotropic. A double-sided estimate for the (n - 1)-dimensional volume of the intersection of a dual p-surface isotropic convex body in terms of its affine invariant dual p-surface quantity is given. Furthermore, the dual p-isopermetric inequality is obtained.