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

Luc Nguyen; Yanyan Li

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arxiv 1212.0460 v1 pith:BELOCANW submitted 2012-12-03 math.AP math.DG

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

YanYan Li , Luc Nguyen This is my paper

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keywords problemyamabeboundcompactnesscurvaturefullygammalower

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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 $\Gamma$ satisfies $\mu^+_\Gamma\le 1$, which includes the $\sigma_k-$Yamabe problem for $k$ not smaller than half of the dimension of the manifold.

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

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