#### Volume 22, issue 6 (2018)

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A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_2$–Yamabe problem

### Matthew Gursky and Jeffrey Streets

Geometry & Topology 22 (2018) 3501–3573
##### Abstract

We define a new formal Riemannian metric on a conformal classes of four-manifolds in the context of the ${\sigma }_{2}$–Yamabe problem. Exploiting this new variational structure we show that solutions are unique unless the manifold is conformally equivalent to the round sphere.

##### Keywords
fully nonlinear Yamabe problem, uniqueness
##### Mathematical Subject Classification 2010
Primary: 58J05
Secondary: 53C44, 58B20