Near-minimizers of the normalized total σ2-curvature on the d-sphere are quantitatively close to the standard metric in two Sobolev norms, with optimal exponents 2 and 4.
Aubin, Equations diff\'erentielles non lin\'eaires et probl\`eme de Y amabe concernant la courbure scalaire , J
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The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form
Near-minimizers of the normalized total σ2-curvature on the d-sphere are quantitatively close to the standard metric in two Sobolev norms, with optimal exponents 2 and 4.