A remark on the gradient map (Q462629)

Summary: For a Hamiltonian action of a compact group \(U\) of isometries on a compact Kähler manifold \(Z\) and a compatible subgroup \(G\) of \(U^{\mathbb C}\), we prove that for any closed \(G\)-invariant subset \(Y\subset Z\) the image of the gradient map \(\mu_{\mathfrak p}(Y)\) is independent of the choice of the invariant Kähler form \(\omega\) in its cohomology class \([\omega]\).