  We study the conformation of a heterogeneous surfactant monolayer at a
fluid-fluid interface, near a boundary between two lateral regions of differing
elastic properties. The monolayer attains a conformation of shallow, steep
`mesas' with a height difference of up to 10 nm. If the monolayer is
progressively compressed (e.g. in a Langmuir trough), the profile develops
overhangs and finally becomes unstable at a surface tension of about K(delta
c_0)^2, where (delta c_0) is the difference in spontaneous curvature and K a
bending stiffness. We discuss the relevance of this instability to recently
observed folding behavior in lung surfactant monolayers, and to the absence of
domain structures in films separating oil and water in emulsions.
