  In order to analyse the lattice dependence of ferromagnetism in the
two-dimensional Hubbard model we investigate the instability of the fully
polarized ferromagnetic ground state (Nagaoka state) on the triangular,
honeycomb and kagome lattices. We mainly focus on the local instability,
applying single spin flip variational wave functions which include majority
spin correlation effects. The question of global instability and phase
separation is addressed in the framework of Hartree-Fock theory. We find a
strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices
(triangular, kagome) for more than half filling. For the triangular lattice we
find the Nagaoka state to be unstable above a critical density of $n=1.887$ at
$U=\infty$, thereby significantly improving former variational results. For the
kagome lattice the region where ferromagnetism prevails in the phase diagram
widely exceeds the flat band regime. Our results even allow the stability of
the Nagaoka state in a small region below half filling. In the case of the
bipartite honeycomb lattice several disconnected regions are left for a
possible Nagaoka ground state.
