Among the various models that have emerged for designing BECs using cold atoms, the potential for bubble trap geometries has been of great interest. In the physics of anisotropic bubble traps in the thin-shell limit, the relationship between the physical parameters and the resulting manifold geometry is not yet fully understood. In this paper, we work towards this goal and show how the parameters of the system must be manipulated to enable the limit of thin shells that do not collapse. Such a restriction leads to dimensional compaction, leading to an effective 2D Hamiltonian associated with the latest bubble trap experiment. Finally, our Hamiltonian is perturbatively solved for some specific cases as an application of our theory.
