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Inequalities of Hessian of distance functions on complete non-compact Riemannian Manifolds

I am interested in finding some inequalities relating the following expression with the curvature on a non-compact Riemannian Manifold $\frac{1}{d_1}Hess^{d_1} (\frac{\partial}{\partial x^\alpha},\...
Teo Rugina's user avatar