Consider an
n
n
-dimensional smooth Riemannian manifold
(
M
n
,
g
)
(M^n,g)
with a given smooth measure
m
m
on it. We call such a triple
(
M
n
,
g
,
m
)
(M^n,g,m)
a Riemannian measure space. Perelman introduced a variant of scalar curvature in his recent work on solving Poincaré’s conjecture
P
(
g
)
=
R
∞
m
(
g
)
=
R
(
g
)
−
2
Δ
g
l
o
g
ϕ
−
|
∇
l
o
g
ϕ
|
g
2
P(g)=R^m_\infty (g) = R(g) - 2\Delta _g log\phi - |\nabla log\phi |^2_g
, where
d
m
=
ϕ
d
v
o
l
(
g
)
dm = \phi dvol(g)
and
R
R
is the scalar curvature of
(
M
n
,
g
)
(M^n,g)
. In this note, we study the topological obstruction for the
ϕ
\phi
-stable minimal submanifold with positive
P
P
-scalar curvature in dimension three under the setting of manifolds with density.