Liouville Theorem for Lichnerowicz Equation on Complete Noncompact Manifolds

Abstract

In this paper, we study the gradient estimates for positive solutions to the Lichnerowicz equation Δ_fu + hu = Au^p + Bu^−q, where h, p, q, A, B are real constants and p > 1, q > 1. Moreover, by these gradient estimates, we can get some very interesting Liouville theorems.