  Minimal surfaces in Euclidean space provide examples of possible non-compact
horizon geometries and topologies in asymptotically flat space-time. On the
other hand, the existence of limiting surfaces in the space-time provides a
simple mechanism for making these configurations compact. Limiting surfaces
appear naturally in a given space-time by making minimal surfaces rotate but
they are also inherent to plane wave or de Sitter space-times in which case
minimal surfaces can be static and compact. We use the blackfold approach in
order to scan for possible black hole horizon geometries and topologies in
asymptotically flat, plane wave and de Sitter space-times. In the process we
uncover several new configurations, such as black helicoids and catenoids, some
of which have an asymptotically flat counterpart. In particular, we find that
the ultraspinning regime of singly-spinning Myers-Perry black holes, described
in terms of the simplest minimal surface (the plane), can be obtained as a
limit of a black helicoid, suggesting that these two families of black holes
are connected. We also show that minimal surfaces embedded in spheres rather
than Euclidean space can be used to construct static compact horizons in
asymptotically de Sitter space-times.
