  The dynamic scaling of curved interfaces presents features that are
strikingly different from those of the planar ones. Spherical surfaces above
one dimension are flat because the noise is irrelevant in such cases. Kinetic
roughening is thus a one-dimensional phenomenon characterized by a marginal
logarithmic amplitude of the fluctuations. Models characterized by a planar
dynamical exponent $z>1$, which include the most common stochastic growth
equations, suffer a loss of correlation along the interface, and their dynamics
reduce to that of the radial random deposition model in the long time limit.
The consequences in several applications are discussed, and we conclude that it
is necessary to reexamine some experimental results in which standard scaling
analysis was applied.
