  We establish mean curvature estimate for immersed hypersurface with
nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar
g)$ through regularity study of a degenerate fully nonlinear curvature equation
in general Riemannian manifold. The estimate has a direct consequence for the
Weyl isometric embedding problem of $(\mathbb S^2, g)$ in $3$-dimensional
warped product space $(N^3, \bar g)$. We also discuss isometric embedding
problem in spaces with horizon in general relativity, like the Anti-de
Sitter-Schwarzschild manifolds and the Reissner-Nordstr\"om manifolds.
