Abstract
Motivated by the joint work of the first author with Khanh and Ngo, and a recent work regarding to a Liouville property of p-Lichnerowicz equation by Zhao, in this paper, we study the following elliptic equation on smooth metric measure spaces (M,g,e−fdv) with a weighted Poincaré inequalityΔp,fv+h(v)=0. We obtain a Liouville type theorem for this equation by using the approach in [11] by the first author and Seo. As a consequence, we are able to point out a Liouville result which is a refinement and improvement of those by Zhao [31].
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