Differentiable convex extensions with sharp Lipschitz constants

Thomas Deck, Carlos Mudarra

Given a superreflexive Banach space $X$, and a set $E\subset X$, we characterise the $1$-jets $(f,G)$ on $E$ that admit $C^{1,\ddot{I}‰}$ convex extensions $(F,DF)$ to all of $X$; where…