  We study the effect of domain perturbation on invariant manifolds for
semilinear parabolic equations subject to Dirichlet boundary condition. Under
Mosco convergence assumption on the domains, we prove the upper and lower
semicontinuity of both the local unstable invariant manifold and the local
stable invariant manifold near a hyperbolic equilibrium. The continuity results
are obtained by keeping track of the construction of invariant manifolds in P.
W. Bates and C. K. R. T. Jones [Dynam. Report. Ser. Dynam. Systems Appl. Vol.
2, 1--38, 1989].
