Large Freiman-homomorphic restriction from bounded derivative images
= Large Freiman-homomorphic restriction from bounded derivative images
Suppose every derivative $x\mapsto\phi(x+d)-\phi(x)$ on $\mathbb F_p^n$ takes at most $C$ values. Then $\phi$ restricts to a Freiman homomorphism on a set of density at least $p^{-1}C^{-5}$. The proof bounds the second-difference image by $C^5$ and chooses a random subspace avoiding its nonzero elements.