  Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc
lattices using a systematic inverse-degeneracy ($1/{\cal N}$) expansion which
incorporates self-energy and vertex corrections such that spin-rotation
symmetry and the Goldstone mode are explicitly preserved. First-order quantum
corrections to magnon energies are evaluated for several cases, providing a
comprehensive picture of the interplay of lattice, band dispersion, and
interaction effects on the stability of the ferromagnetic state with respect to
both long- and short-wavelength fluctuations. Our results support the belief
that ferromagnetism is a generic feature of the Hubbard model at intermediate
and strong coupling provided the DOS is sufficiently asymmetric and strongly
peaked near band edge, as for fcc lattice with finite $t'$. For
short-wavelength modes, behavior of a characteristic energy scale $\omega^*
\sim T_c$ (magnon-DOS-peak energy) is in excellent agreement with the $T_c$ vs.
$n$ behavior within DMFT, both with respect to the stable range of densities
($0.20 < n < 0.85$) as well as the optimal density $n=0.65$. However, our
finding of vanishing spin stiffness near optimal density highlights the role of
long-wavelength fluctuations in further reducing the stable range of densities.
