  Domains and bubbles in tilted phases of Langmuir monolayers contain a class
of textures knows as boojums. The boundaries of such domains and bubbles may
display either cusp-like features or indentations. We derive analytic
expressions for the textures within domains and surrounding bubbles, and for
the shapes of the boundaries of these regions. The derivation is perturbative
in the deviation of the bounding curve from a circle. This method is not
expected to be accurate when the boundary suffers large distortions, but it
does provide important clues with regard to the influence of various energetic
terms on the order-parameter texture and the shape of the domain or bubble
bounding curve. We also look into the effects of thermal fluctuations, which
include a sample-size-dependent effective line tension.
