Existence of rotationally symmetric embedded f-minimal tori

We generalize Angenent's shrinking tori \cite{Angenent1992} to minimal $n$-dimensional tori embedded in $\mathbb{R}^{n+1}$ equipped with the metric $$g=e^{-\frac{f(\sum^{n+1}_{i=1}x_{i}^{2})}{2n}}\sum^{n+1}_{i=1}dx^{2}_{i},$$ where $f$ is a convex function and $f'$ is bounded above and below by positive constants.