Is the function $f(x,y) = \frac{x}{y}$ convex in the region $x, y > 0$?
I think the Hessian matrix is not positive semidefinite and the function is not convex as well:
\begin{equation} H =\begin{bmatrix} 0 & -\frac{1}{y^2} \\ -\frac{1}{y^2} & \frac{2x}{y^3}\\ \end{bmatrix} \end{equation}
Am I right?
