On a conformally invariant functional of the space of Riemannian metrics (Q1062020)

The author studies the variational theory of the conformal invariant functional \(\nu (g)=(2/n)\int_{M}| W_ g|^{n/2}\nu_ g\) of Riemann metrics g on a compact n-manifold M, where \(W_ g\) is the Weyl tensor of g; special attention is given to the case \(n=4\). Significant lower bounds are provided for \(\inf_ g\nu (g)=\nu (M)\). Along with several examples, it is shown that \(\nu\) (M) is subadditive with respect to connected sums.