Willmore surfaces in the unit \(n\)-sphere
This paper proves a kind of gap theorem for Willmore surfaces in the sphere. Namely, if the square of the norm \(\Phi\) of the traceless second fundamental form is pinched between \(0\) and a certain constant depending on the length of the mean curvature vector, then \(\Phi\) can only have one of the extreme values. In each of the cases, the surfaces are classified. Several examples are also given.
scientific article; zbMATH DE number 2148909