In this paper we extend the results of Kirwan et alii on convexity properties of the moment map for Hamiltonian group actions, and on the connectedness of the fibers of the moment map, to the case of non-compact orbifolds.Our motivation is twofold. First, the category of orbifolds is important in symplectic geometry because, generically, the symplectic quotient of a symplectic manifold is an orbifold. Second, our proof is conceptually very simple since it reduces the non-abelian case to the abelian case.

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