Corollary: Conditional regularity transfer

Under Theorem thm:transfer, independent verification of hyp:exp implies that the common limiting front has no flat boundary segment and has a $C^1$ boundary. Independent verification of hyp:gamma, for a Gamma target, implies the $C^1$ conclusion, but not the no-flat-segment conclusion.

Proof. The theorem identifies the limiting body with a positive scalar multiple of the target body. Positive dilation preserves strict convexity and $C^1$ regularity. The Gamma assertion contains no strict-convexity hypothesis.