  In the first part of the paper, we build a foundation for further work on
Hamiltonian actions on symplectic orbifolds. Most importantly we prove the
orbifold versions of the abelian connectedness and convexity theorems.
  In the second half, we prove that compact symplectic orbifolds with
completely integrable torus actions are classified by convex simple rational
polytopes with a positive integer attached to each facet and that all such
orbifolds are algebraic toric varieties.

Differential Geometry;Differential Geometry