  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 domains 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(dc)^2 (dc being the difference in spontaneous curvature and K a
bending modulus). In addition, the boundary is found to undergo a
topography-induced rippling instability upon compression, if its line tension
is smaller than about K(dc). The effect of diffuse boundaries on these features
and the topographic behavior near a critical point are also examined. We
discuss the relevance of our findings to several experimental observations
related to surfactant monolayers: (i) small topographic features recently found
near domain boundaries; (ii) folding behavior observed in mixed phospholipid
monolayers and model lung surfactants; (iii) roughening of domain boundaries
seen under lateral compression; (iv) the absence of biphasic structures in
tensionless surfactant films.
