  The geometry of a two-dimensional surface in a curved space can be most
easily visualized by using an isometric embedding in flat three-dimensional
space. Here we present a new method for embedding surfaces with spherical
topology in flat space when such a embedding exists. Our method is based on
expanding the surface in spherical harmonics and minimizing for the differences
between the metric on the original surface and the metric on the trial surface
in the space of the expansion coefficients. We have applied this method to
study the geometry of back hole horizons in the presence of strong,
non-axisymmetric, gravitational waves (Brill waves). We have noticed that, in
many cases, although the metric of the horizon seems to have large deviations
from axisymmetry, the intrinsic geometry of the horizon is almost axisymmetric.
The origin of the large apparent non-axisymmetry of the metric is the
deformation of the coordinate system in which the metric was computed.

General Relativity and Quantum Cosmology