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It is a well known fact that, if $\Sigma$ is an Einstein hypersurface withpositive scalar curvature, then it is a round sphere. We give a stable versionof 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 resultis given in a quantitative way.

Quantitative $W^{2, \, p}$-stability for almost Einstein hypersurfaces