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Variational structure of the \(v_{\frac{n}{2}}\)-Yamabe problem. (English) Zbl 1383.53028

Summary: We define a formal Riemannian metric on a conformal class in the context of the \(v_{\frac{n}{2}}\)-Yamabe problem. We also give a new variational description of this problem, and show that the associated functional is geodesically convex. Formal properties of the negative gradient flow are also described. These results parallel our work in two dimensions on the Liouville energy and the uniformization of surfaces, and our work in four dimensions on the \(\sigma_2\)-Yamabe problem in two preprints.

MSC:

53C20 Global Riemannian geometry, including pinching
58E11 Critical metrics
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