It is a well known fact that, if $\Sigma$ is an Einstein hypersurface with positive scalar curvature, then it is a round sphere. We give a stable version of this result showing that if a hypersurface is almost Einstein in a $L^p$-sense, then it is $W^{ 2, \, p}$ - close to the round sphere. The result is given in a quantitative way.
Categories: math.DG