For any convex f whose derivative is bounded between two positive constants, there exist rotationally symmetric embedded f-minimal n-tori in the given conformal metric on R^{n+1}.
Eigenvalue estimate and compactness for closedf-minimal surfaces.Pacific Journal of Mathematics, 271(2):347–367
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Existence of rotationally symmetric embedded f-minimal tori
For any convex f whose derivative is bounded between two positive constants, there exist rotationally symmetric embedded f-minimal n-tori in the given conformal metric on R^{n+1}.