A formal Riemannian structure on conformal classes and uniqueness for the σ2–Yamabe problem

Gursky, Matthew¹ ; Streets, Jeffrey²

¹ Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States
² Department of Mathematics, University of California, Irvine, Irvine, CA, United States

Geometry & topology, Tome 22 (2018) no. 6, pp. 3501-3573.

Résumé

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.

Détail

DOI : 10.2140/gt.2018.22.3501

Classification : 58J05, 53C44, 58B20
Keywords: fully nonlinear Yamabe problem, uniqueness

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