Geometric effects on fluctuating droplets in curved surfaces

Nucleation processes occur during first-order transitions and arise because of the metastability of a preexisting phase; a phenomenon ubiquitous in nature. Considering an order parameter with a prescribed Landau-Ginzburg energy, which may represent the relative density of liquid-vapor phases or the degree of crystallization of uniform-crystalline phases, we move to an interface representation of the nucleated droplets. By an expansion in small perturbations away from circular droplets we investigate the effects of the underlying geometry on the line tension arising from thermal fluctuations.