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 $$g=e^{-\frac{f(\sum _{i=1}^{n+1}{x}_i^2)}{2n}}\sum _{i=1}^{n+1}d{x}_i^2,$$ where $f$ is a convex function and $f^{\mathrm{\prime }}$ is bounded above and below by positive constants.