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

Gursky, Matthew; Streets, Jeffrey

doi:10.2140/gt.2018.22.3501

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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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

DOI: 10.2140/gt.2018.22.3501

Abstract

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.

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

Volume 22, issue 6 (2018)