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

Yazhou Han, Meijun Zhu

Published 2015-02-07Version 1

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.