  In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface
consisting of a one-parameter family of spacelike submanifolds. Recently,
Bousso and Randall introduced the notion of caustics of world hyper-sheets in
order to define the notion of holographic domains in space-time. Here, we give
a mathematical framework for describing the caustics of world hyper-sheets in
the Minkowski space-time. As a consequence, we investigate the singularities of
the caustics of world hyper-sheets and whose geometrical meanings. Although the
Minkowski space-time has zero gravity, this framework gives a simple toy model
for general cases.
