On closed manifolds with Y1>0 and Y2>0, the σ2-Yamabe infimum is achieved by a conformal metric with R_g>0, and the two infima with and without the σ2>0 restriction coincide.
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The $\sigma_k$-Yamabe problem revisited
On closed manifolds with Y1>0 and Y2>0, the σ2-Yamabe infimum is achieved by a conformal metric with R_g>0, and the two infima with and without the σ2>0 restriction coincide.