  The superradiant stability of asymptotically flat D-dimensional extremal
Reissner-Nordstrom black holes under charged massive scalar perturbation is
analytically studied. Recently, an analytical method has been proposed by the
author and used to prove that five and six-dimensional extremal
Reissner-Nordstrom black holes are superradiantly stable under charged massive
scalar perturbation. We apply this analytical method in the D-dimensional
extremal Reissner-Nordstrom black hole cases and prove that the D-dimensional
Reissner-Nordstrom black holes are all superradiantly stable under charged
massive scalar perturbation. Our result is consistent with the previous
numerical observation in the literature and provides a rigorous analytical
proof.
