Optimal rigidity estimates for varifolds almost minimizing the Willmore energy

For an integral $2$-varifold V=v(Σ,θ≥ 1) in Rⁿ with generalized mean curvature H∈ L² such that μ(Rⁿ)=4π and ∫Σ|H|²dμ≤ 16π(1+δ²) , we show that Σ is W2,2 close to the standard embedding of the round sphere in a quantitative way when δ< δ₀ 1. For $n=3$, we prove that the sharp constant is δ₀²=2π.