  In this paper, by mainly using the rearrangement technique and suitably
constructing trial functions, under the constraint of fixed weighted volume, we
can successfully obtain several isoperimetric inequalities for the first and
the second Dirichlet eigenvalues, the first nonzero Neumann eigenvalue of the
Witten-Laplacian on bounded domains in space forms. These spectral
isoperimetric inequalities extend those classical ones (i.e. the Faber-Krahn
inequality, the Hong-Krahn-Szeg\H{o} inequality and the Szeg\H{o}-Weinberger
inequality) of the Laplacian.
