Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces

Abstract

Abstract In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space ( M , ⟨ , ⟩ , e − ϕ d v ) \\left(M,\\langle ,\\rangle ,{e}^{-\\phi }{\\rm{d}}v) , with nonnegative weighted Ricci curvature Ric ϕ ≥ 0 {{\\rm{Ric}}}^{\\phi }\\ge 0 for some ϕ ∈ C 2 ( M ) \\phi \\in {C}^{2}\\left(M) , which is uniformly bounded from above, and successfully obtain several universal inequalities of this eigenvalue problem.