Abstract
Let
(X,ω)
be an
n
-dimensional compact Kähler manifold. We study degenerate complex Hessian equations of the form
(ω+d
d
c
φ
)
m
∧
ω
n−m
=F(x,φ)
ω
n
.
Under some natural conditions on
F
, this equation has a unique continuous solution. When
(X,ω)
is rational homogeneous we further show that the solution is Hölder continuous.