English

A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound

Analysis of PDEs 2014-10-14 v1 Differential Geometry

Abstract

We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions when the associated cone Γ\Gamma satisfies μΓ+1\mu^+_\Gamma\le 1, which includes the σk\sigma_k-Yamabe problem for kk not smaller than half of the dimension of the manifold.

Keywords

Cite

@article{arxiv.1212.0460,
  title  = {A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound},
  author = {YanYan Li and Luc Nguyen},
  journal= {arXiv preprint arXiv:1212.0460},
  year   = {2014}
}
R2 v1 2026-06-21T22:47:58.957Z