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Gromov-Hausdorff Stability and Rigidity of manifolds via Heisenberg-Pauli-Weyl Uncertainty Principle
The classical Heisenberg Pauli Weyl (HPW) inequality exhibits a strong rigidity phenomenon on Riemannian manifolds i.e. on Cartan Hadamard manifolds and those with non-negative Ricci curvature, the validity of the Euclidean HPW inequality or the existence of extremizers strictly forces the manifold
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