Liouville-type theorem for the drifting Laplacian operator
Consider a manifold \((M, g, e ^{-f} dV)\) with a smooth measure. The authors obtain gradient estimates for positive harmonic functions of the drifting Laplacian. If the \(\infty\)-Bakry-Emery Ricci tensor is bounded from below and \(|\nabla f|\) is bounded, they obtain a Liouville-type theorem, extending in this way the classical result by \textit{S. Y. Cheng} and \textit{S.-T. Yau} [Commun. Pure Appl. Math. 28, 333--354 (1975; Zbl 0312.53031)].
scientific article; zbMATH DE number 5902955
scientific article