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$\boldsymbol {L^p}$-HARDY AND 
$\boldsymbol {L^p}$-RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS
In this paper we obtain some improved 
$L^p$-Hardy and 
$L^p$-Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.
