Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications

Abstract

In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach. Even for the classic Yamabe problem on locally conformally flat manifolds, our approach provides a new and relatively simpler solution.

References in corpus (4)

• Sign of Green's function of Paneitz operators and the Q curvature
• Prescribing integral curvature equation
• One Dimensional Conformal Metric Flows
• One dimensional conformal metric flow II

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• Subcritical Approach to Sharp Hardy-Littlewood-Sobolev Type Inequalities on the Upper Half Space
• Sharp reversed Hardy-Littlewood-Sobolev inequality with extended kernel