Analytical solutions are presented to describe the hydromagnetic support of quiescent solar prominences treated as cold plasma sheets in the characteristic normal and inverse configurations. The solar corona is modeled to be axisymmetric outside a unit sphere, with the prominence sheet lying in the equatorial plane extending from the sphere out to a finite radial distance subject to an inverse-square Newtonian gravity. The relationship between prominence support and the global topology of the surrounding poloidal magnetic field is discussed, with a particular interest in the role of magnetic flux ropes in the support of inverse prominences A novel solution is also studied describing a rope of purely azimuthal magnetic flux held in equilibrium by the weight of an internal distribution of cold mass and by an external poloidal magnetic field rigidly anchored to the base of the model corona. This solution illustrates the role that prominence weight may play in storing magnetic energy for driving coronal mass ejections.
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