It is known that, in string sigma-model metric, the 'extreme' fivebran
e solution of D = 10 supergravity interpolates between D = 10 Minkowsk
i spacetime and a supersymmetric S3 compactification to a linear dilat
on vacuum. We show here that, in fivebrane sigma-model metric, the ext
reme string solution of D = 10 supergravity interpolates between Minko
wski spacetime and a hitherto unknown supersymmetric S7 compactificati
on of d = 10 supergravity to a three-dimensional anti-de Sitter genera
lization of the linear dilaton vacuum, which may be invariantly charac
terized in terms of conformal Killing vectors. The dilaton field diver
ges near the string core but this divergence may be eliminated by re-i
nterpreting the string solution as the extreme membrane solution of 11
-dimensional supergravity. We show that the latter has an analytic ext
ension through a regular degenerate event horizon to an interior regio
n containing a curvature singularity. We obtain analogous results for
other extended object solutions of supergravity theories.