Gradient Estimates for p-Laplacian Lichnerowicz Equation on Noncompact Metric Measure Space

In this paper, the authors obtain the gradient estimates for positive solutions to the weighted p-Laplacian Lichnerowicz equation Delta p,fu+cu sigma=0 = 0$$\end{document} on noncompact smooth metric measure space, where c is a nonnegative constant, and p, sigma (1 < p <= 2, sigma <= p - 1) are real constants. Moreover, by the gradient estimate, they can get the corresponding Liouville theorem and Harnack inequality.