  The dense neutrino medium in a core-collapse supernova or a neutron-star
merger event can experience fast flavor conversions on time/distance scales
that are much smaller than those of vacuum oscillations. It is believed that
fast neutrino flavor transformation occurs in the region where the angular
distributions of $\nu_e$ and $\bar\nu_e$ cross each other. We present the first
study of this crossing phenomenon and the fast neutrino flavor conversions in
multidimensional (multi-D) supernova models. We examine the neutrino
distributions obtained by solving the Boltzmann transport equation for several
fixed profiles which are representative snapshots taken from separate 2D and 3D
supernova simulations with an $11.2 M_\odot$ progenitor model. Our research
shows that the spherically asymmetric patterns of the $\nu_e$ and $\bar\nu_e$
fluxes in multi-D models can assist the appearance of the crossing between the
$\nu_e$ and $\bar\nu_e$ angular distributions. In the models that we have
studied, there exist unstable neutrino oscillation modes in and beyond the
neutrino decoupling region which have amplitude growth rates as large as an
$e$-fold per nanosecond. This finding can have important consequences for the
explosion mechanism, nucleosynthesis, and neutrino signals of core-collapse
supernovae.
