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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 σ2–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
References
Publication
Received: 12 June 2017
Revised: 29 September 2017
Accepted: 10 November 2017
Published: 23 September 2018
Proposed: Simon Donaldson
Seconded: Bruce Kleiner, Tobias H Colding
Authors
Matthew Gursky
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States
Jeffrey Streets
Department of Mathematics
University of California, Irvine
Irvine, CA
United States