A Hubbard model with a single, partially Aat band has ferromagnetic ground
states. It is shown that local stability of ferromagnetism implies its glob
al stability in such a model: The model has only ferromagnetic ground state
s if there are no single spin-flip ground states. Since a single-band Hubba
rd model away from half filling describes a metal, this result may open a r
oute to metallic ferromagnetism in single-band Hubbard models. [S0031-9007(
99)09222-4].