  The usual theory of inflation breaks down in eternal inflation. We derive a
dual description of eternal inflation in terms of a deformed Euclidean CFT
located at the threshold of eternal inflation. The partition function gives the
amplitude of different geometries of the threshold surface in the no-boundary
state. Its local and global behavior in dual toy models shows that the
amplitude is low for surfaces which are not nearly conformal to the round
three-sphere and essentially zero for surfaces with negative curvature. Based
on this we conjecture that the exit from eternal inflation does not produce an
infinite fractal-like multiverse, but is finite and reasonably smooth.
