A formal Riemannian structure on conformal classes and uniqueness for the ${\sigma }_2$-Yamabe problem

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.

Cited by in corpus (2)

• Local pointwise second derivative estimates for strong solutions to the ${\sigma }_k$-Yamabe equation on Euclidean domains
• ${\sigma }_2$ Yamabe problem on conic spheres II:boundary compactness of the moduli