Improved Multipolar Poincar\'e-Hardy inequalities on Cartan-Hadamard Manifolds

We prove a family of improved multipolar Poincar'e-Hardy inequalities on Cartan-Hadamard manifolds. For suitable configurations of poles, these inequalities yield an improved multipolar Hardy inequality and an improved multipolar Poincar'e inequality such that the critical unipolar singular mass is reached at any pole.