  We show by matching two flat spaces one in Minkowski coordinates ( empty
space) and the other in Minkowski coordinates after a special conformal
transformation (also empty space) through a bubble with positive and constant
surface tension, that the motion of the bubble is hyperbolic. If the surface
tension is very big the initial size of the bubble is as small as we wish, so
that we can indeed obtain an infinite universe out of empty spaces. The induced
space in the bubble is de Sitter type.
