  Geometrical structure of matter at subnuclear densities is investigated in
the presence of a degenerate gas of neutrinos as encountered in stellar
collapse. The crystalline phases with spherical, cylindrical and planar nuclei
as well as with spherical and cylindrical nuclear bubbles are considered by
using a compressible liquid-drop model. This model allows for uncertainties in
the lepton fraction $Y_{\rm L}$ in addition to those in the nuclear surface
tension $E_{\rm surf}$ and in the proton chemical potential in bulk neutron
matter $\mu_{\rm p}^{(0)}$. The phase diagrams obtained at zero temperature
show that only the phases with rod-like and slab-like nuclei occur at typical
values of $Y_{\rm L}$, $E_{\rm surf}$ and $\mu_{\rm p}^{(0)}$, whereas the
bubble phases, especially with spherical bubbles, are at best expected at
hypothetically low values of $Y_{\rm L}$ and/or $E_{\rm surf}$. For the
rod-like and slab-like nuclei, thermally induced displacements are calculated
from their respective elastic constants. It is found that at temperatures
appropriate to supernova cores, thermal fluctuations would destroy the layered
lattice of slab-like nuclei almost independently of the nuclear models and of
the degree of the neutrino degeneracy.
