Han-Wen Liu

On the Hessian Conjecture in Lorentzian Signature: Constant Pivots and Hesse Systems

As a close relative of the Jacobian conjecture, the Hessian conjecture in dimension $n$ states that the local Legendre transform of a polynomial solution to the Monge--Amp\`ere equation $\det(\operatorname{Hess}(\phi))=\pm1$ is also a polynomial solution. The general Hessian conjecture is false for $n\geq5$, while in R...