| Abstract: |
| Riccati pairs allow us to establish Hardy inequalities on Riemannian manifolds by solving corresponding Riccati-type ordinary differential inequalities. This method relies solely on simple convexity arguments, the divergence theorem, and the Laplace comparison theorem. Moreover, it is symmetrization-free, making it broadly applicable: inequalities formulated on model space forms extend naturally to general manifolds with lower sectional curvature. |
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