Liouville property for $f$-harmonic functions with polynomial growth (1610.03923v3)

Abstract: We prove a Liouville property for any $f$-harmonic function with polynomial growth on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ when the Bakry-\'Emery Ricci curvature is nonnegative and its diameter of geodesic sphere has sublinear growth.