2 problems

Anisotropic KPZ conjecture. If the Hessian matrix $D^2v(\rho)$ has two eigenvalues of the same sign, equivalently if $\det(D^2v(\rho))>0$, then

Let $v(\cdot)$ be the speed function of a reasonable $(2+1)$-dimensional growth model, and let $H_\rho$ be the Hessian of $v(\cdot)$ computed at the slope $\rho$. Write $\alpha$ fo…