  Motivated by the fact that many physical landscapes are characterized by
long-range height-height correlations that are quantified by the Hurst exponent
H, we investigate the statistical properties of the iso-height lines of
correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We
show numerically that in the continuum limit the external perimeter of a
percolating cluster of correlated surfaces with H between -1 and zero is
statistically equivalent to SLE curves. Our results suggest that the external
perimeter also retains the Markovian properties, confirmed by the absence of
time correlations in the driving function and the fact that the latter is
Gaussian distributed for any specific time. We also confirm that for all H the
variance of the winding angle grows logarithmically with size.
