We theoretically study the topography of a biphasic surfactant monolayer in
the vicinity of domain boundaries. The differing elastic properties of the
two phases generally lead to a nonflat topography of "mesas," where domain
s of one phase are elevated with respect to the other phase. The mesas are
steep but low, having heights of up to 10 nm. As the monolayer is laterally
compressed, the mesas develop overhangs and eventually become unstable at
a surface tension of about K(deltac(o))(2) (deltac(o) being the difference
in spontaneous curvature and K a bending modulus). In addition, the boundar
y is found to undergo a topography-induced rippling instability upon compre
ssion. if its line tension is smaller than about K deltac(o). The effect of
diffuse boundaries on these features and the topographic behavior near a c
ritical point are also examined. We discuss the relevance of our findings t
o several experimental observations related to surfactant monolayers: ii) s
mall topographic features recently found near domain boundaries: (ii) foldi
ng behavior observed in mixed phospholipid monolayers and model lung surfac
tants: (iii) roughening of domain boundaries seen under lateral compression
: (iv) the absence of biphasic structures in tensionless surfactant films.