  Some of the most known integral inequalities are the Sobolev, Hardy and
Rellich inequalities in Euclidean spaces. In the context of submanifolds, the
Sobolev inequality was proved by Michael-Simon and Hoffman-Spruck. Since then,
a sort of applications to the submanifold theory has been derived from those
inequalities. Years later, Carron obtained a Hardy inequality for submanifolds
in Hadamard spaces. In this paper, we prove the general Hardy and Rellich
Inequalities for submanifolds in Hadamard spaces. Some applications are given
and we also analyse the equality cases.
