  We study the scaling properties of self-flattening surfaces under global
suppression on surface fluctuations. Evolution of self-flattening surfaces is
described by restricted solid-on-solid type monomer deposition-evaporation
model with reduced deposition (evaporation) at the globally highest (lowest)
site. We find numerically that equilibrium surface fluctuations are anomalous
with roughness exponent $\alpha\simeq 1/3$ and dynamic exponent $z_W \simeq
3/2$ in one dimension (1D) and $\alpha=0 (\log)$ and $z_W \simeq 5/2$ in 2D.
Stationary roughness can be understood analytically by relating our model to
the static self-attracting random walk model and the dissociative dimer type
deposition-evaporation model. In case of nonequilibrium growing/eroding
surfaces, self-flattening dynamics turns out to be irrelevant and the normal
Kardar-Parisi-Zhang universality is recovered in all dimensions.
