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Finite domains of a Langmuir monolayer in a phase with tilted molecules canbe modeled by a simple elastic free energy of an XY order parameter withisotropic and anisotropic line tension terms. The domains can and often docontain nontrivial textures, which in turn influence the shape of the domains.Herein we investigate the properties of a simplified isotropic model with asingle elastic constant. For circular domains a first-order phase transition isfound between two distinct textures: an exterior defect (or ``virtual boojum'')texture, and an interior defect texture. Starting with a circular domain andeither of these two textures as a ground state, we find shape instabilitiesdevelop that depend on the elastic constants and line tensions in thesimplified model. In both cases a necessary but not sufficient condition forthe onset of shape instabilities is the possibility for a local negativeeffective line tension to develop from the anisotropic line tension term.Comment: 14 double column RevTex pages, 8 eps figure

Stability of texture and shape of circular domains of Langmuir monolayers