Affiliation:
1. Faculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University , Wuhan 430062 , China
2. School of Mathematics and Physics Science, Jingchu University of Technology , Jingmen , 448000 , China
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.
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