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

Abstract

In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space (M,⟨,⟩,e−ϕdv)\left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v), with nonnegative weighted Ricci curvature Ricϕ≥0{{\rm{Ric}}}^{\phi }\ge 0 for some ϕ∈C2(M)\phi \in {C}^{2}\left(M), which is uniformly bounded from above, and successfully obtain several universal inequalities of this eigenvalue problem.

Keywords

• eigenvalues
• universal inequalities
• poly-drifting laplacian
• smooth metric measure space
• weighted ricci curvature
• 35p15
• 53c20
• 53c42