Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in euklidean spaces - Scheuer, Julian (Bulletin of the Australian Mathematical Society, 2015)
We prove ϵ{epsilon}-closeness of hypersurfaces to a sphere in Euclidean space under the assumption that the traceless second fundamental form is δ{delta} small compared to the mean curvature. We give the explicit dependence of δ{delta} on ϵ{epsilon} within the class of uniformly convex hypersurfaces with bounded volume.
Gesehen am 18.06.2020