  We study the dynamics of vortices formed in a superfluid film adsorbed on the
curved two-dimensional surface of a cone. To this aim, we observe that a cone
can be unrolled to a sector on a plane with periodic boundary conditions on the
straight sides. The sector can then be mapped conformally to the whole plane,
leading to the relevant stream function. In this way, we show that a superfluid
vortex on the cone precesses uniformly at fixed distance from the apex. The
stream function also yields directly the interaction energy of two vortices on
the cone. We then study the vortex dynamics on unbounded and bounded cones. In
suitable limits, we recover the known results for dynamics on cylinders and
planar annuli.
