Existence of rotationally symmetric embedded f-minimal tori

We generalize Angenent's shrinking torus \cite{Angenent1992} by proving the existence of an embedded $n$-dimensional $f$-minimal hypersurface diffeomorphic to $S^1\times S^{n-1}$ in $\mathbb{R}^{n+1}$ equipped with the metric $$ds^{2}=e^{-\frac{f(|x|^2)}{2n}}{\sum^{n+1}_{i=1}dx^{2}_{i}},$$ where $f$