We show that the measurements of 10 GeV atmospheric neutrinos by an upcoming array of densely packed phototubes buried deep inside the IceCube detector at the South Pole can be used to determine the neutrino mass hierarchy for values of sin^2(2theta13) close to the present bound, if the hierarchy is normal. These results are obtained for an exposure of 100 Mton years and systematic uncertainties up to 10%.
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