This is a kind of a follow-up to Question on Hessian of a function (probability question). Suppose I give you a continuous function $ f:\mathbb{R}^n \to \mathbb{R}.$ Is it true that there exists a ($ C^2$ ) function $ g:\mathbb{R}^n \to \mathbb{R},$ such that $ \det(\mbox{Hess}(g)) = f?$ (where $ \mbox{Hess}$ is the Hessian, ofRead more