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We prove that, for every closed (not necessarily convex) hypersurface Σ in ℝn+1{\mathbb{R}^{n+1}} and every p>n{p>n}, the Lp{L^{p}}-norm of the trace-free part of the anisotropic second fundamental form controls from above the W2,p{W^{2,p}}-closeness of Σ to the Wulff shape. In the isotropic setting, we provide a simpler proof. This result …