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

By Yanyan Li, Luc Nguyen. 2012

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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 satisfies μ Γ + ⩽ 1 , which includes the σ k -Yamabe problem for k not smaller than half of the dimension of the manifold.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c026c5485bee3c78cf10d6192f01fae280b17079