A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_{2}$-Yamabe problem
Differential Geometry
2018-10-03 v1 Analysis of PDEs
Abstract
We define a new formal Riemannian metric on a conformal classes of four-manifolds in the context of the -Yamabe problem. Exploiting this new variational structure we show that solutions are unique unless the manifold is conformally equivalent to the round sphere.
Cite
@article{arxiv.1603.07005,
title = {A formal Riemannian structure on conformal classes and uniqueness for the $\sigma_{2}$-Yamabe problem},
author = {Matthew J. Gursky and Jeffrey Streets},
journal= {arXiv preprint arXiv:1603.07005},
year = {2018}
}