Geometry & Topology

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

Matthew Gursky and Jeffrey Streets

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

Article information

Geom. Topol., Volume 22, Number 6 (2018), 3501-3573.

Received: 12 June 2017
Revised: 29 September 2017
Accepted: 10 November 2017
First available in Project Euclid: 29 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 58B20: Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]

fully nonlinear Yamabe problem uniqueness


Gursky, Matthew; Streets, Jeffrey. A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_2$–Yamabe problem. Geom. Topol. 22 (2018), no. 6, 3501--3573. doi:10.2140/gt.2018.22.3501.

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